Actually, I do have apply a Sch diode SS34-1n5822 at that p-mos placing.

Did you replace both PMOS devices?

The ripple voltage on that E-cap change from 150mV-->~137mV.

What current did you calculate from that ripple voltage?

Murata have a useful tool for this stuff https://ds.murata.co.jp/simsurfing/index.html?lcid=en-us

Yes, nice tools from some of the larger suppliers.

Also your 25V MLCC caps running at 15V will be at about 40% of rated value.

I've seen much worse even from reputable suppliers.  Just looked at that tool for 22uF 25V X5S parts.  Only one showed up: GRM188C61E226ME01.  It drops to 10% of rated value by 15V.

Alan,

Certainly could be any such possibility.  My only glass glowing experience was in college and shortly after, in other words, decades ago.  Was going mostly on the one image which looks like cracked glass.

I'm looking at what kind of core material for the GDT but I haven't found much relevant information or they are hidden somewhere in there. How do I determine the size of the core, and how do I select its material. Can MnZn or NiZn be used or must it have a permeability that adjusts to the operating frequency of the TC?

    https://highvoltageforum.net/index.php?topic=1854.msg13949#msg13949
NiZn is rarely used below 1MHz due to higher loss.  Advantage for some cases is it's an electrical insulator at room temperature.  (But not when hot.)

Also, the igbt that I plan to use is the IXGR50N60BD1, which has a gate voltage of +-20V. Can it be operated at 20v or should I be a little lower, like 18v?

+-24V is fine if you want to push current.  20V limit is for high reliability under continuous use for years.  TCs typically operate for a few hours total ever.
Looks like an obsolete IGBT part.  Is it fast enough for 300-400kHz even with ZCS operation?  (And parts from EBay etc. are often counterfeit, so may be slower or not be robust at rated current.)

Most voltage spiking is caused by parasitic inductance.  The most important two ways to minimize chance of spike damage are:
1) Use IGBTs well below specified maximum Vce.  Most IGBT parameters such as switching energy are specified at half of max Vce.  That's a typical operating condition.  Thus if you are using 230Vac input into bridge rectifier, Vbus will be 325V.  IGBTs rated for 650Vce max would be a good choice.  600V IGBTs may be fine if second condition is met:
2) Minimize interconnect inductance of bridge.  Inductance internal to IGBT packages can't be eliminated.  Most external inductance can be minimized.  Here's my tutorial showing one good half-bridge layout (and full-bridge farther down in thread):
    https://highvoltageforum.net/index.php?topic=1324.msg9795#msg9795
Many designs have no additional components for Vce spike protection.  (Vge clamping with smaller 500W or 600W TVS diodes is still recommended, with TVS diodes soldered close to IGBT G and E terminals.)
There are some cases on this forum where TVS diodes failed first, then failed diode destroyed IGBT.  TVS diodes usually fail to shorted, so overload opposite IGBT.  IGBTs sometimes handle more transient power than do TVS diodes.
TVS diodes and RCD snubbers help only if their interconnect inductance is lower or at least similar to that of bridge interconnect.  That's why it is usually better to just lower bridge inductance.
R+C snubbers can reduce spikes further if inductance can't be reduced enough.  But R+C snubbers dissipate more power in general.
TVS diode capacitance is low enough that it will have no significant impact on coil performance (in case you decide to use TVS diodes on Vce).
Being your first coil, I'd also suggest:
    https://highvoltageforum.net/index.php?topic=2191.msg16147#msg16147
Good cooling is important for IGBT survival.  For even better cooling, you could consider adding heat spreader plates below IGBTs or electrically-live heat sinks.  And good thermal past for whatever configuration you use.

But with the current IGBTs I'm pretty sure that these are just some local guy stripping some inverters or something and making a bit of money. I got a bunch of random 100A, 150A and also some 75A and 200A modules from him that still had the old gate circuitry on them.

Does sound likely to be genuine given old gate drive circuitry etc.  I have purchased counterfeit IGBTs of TO247 variety from EBay (and gotten refunds after proving data sheet spec's weren't met).  Your situation sounds different enough.

There should be no issues with the matching transformer - at 43.5kHz and 7 turns I get a flux density of 314mT, which still leaves me with a fair amount of head room given a maximum flux density of 380mT for the K4000 material. At the time of failure I used twice the amount of turns, so saturation should be pretty much impossible.

Probably not, but I don't know enough about UD+ to be certain.  Controlling by secondary current leaves the possibility of sub-harmonic component that builds up excess current due to resonance of primary coupling capacitor set with transformer inductance.  Might be safer to control by primary current.

What I noticed was that on the bus caps, one screw turned out to be loose (on the connection between the two series caps). There was still contact however, and I do not think that lacking a bus cap would lead to my bridge exploding randomly after a day of testing anyway.

Hard to say when some jarring or magnetically induced force from current may have made momentary disconnects.  I'd inspect that connection for any subtle signs of arcing - black residue or pitting.  Loose power connections are often problematic.

I did notice a strange kind of ringing however, both in normal operation and in freewheeling mode (tested with signal generator / scope). Where does that come from, and is it dangerous? The dip in the middle is not really that deep and looking at the data sheet, the IGBT only starts conducting at 6V so that amount of ringing should not pose much of an issue yet. Nevertheless I want to get rid of it of course, any tips?

I'm guessing this is Vge ringing.  Not specified.  If so, scope images are needed to make any useful recommendations.

As I was writing this I remembered that when I was checking gate wave forms sometime earlier, I managed to produce a ground loop from one emitter through my scope lead, popping the breaker (I forgot to remove the scope lead when switching from the isolation transformer to regular mains). I am pretty sure this happened to be the same IGBT that is now shorted, could that have damaged the gate somehow?

This would be first guess as to a cause.  Presuming scope ground was connected to smaller Kelvin emitter pin (pin paired with gate pin), resistance of that path might be high enough to fry something with momentary fault current.  (Second guess is above loose power connection.)
BTW, I made the almost-same mistake once too, forgetting to remove scope ground when switching from isolated to line power.  Wasn't on gate return, so didn't fry anything.  Was a bit surprised that scope and probe both survived too.

And last of all, the ebay seller I got these from did not take any measures against ESD and just packed them into refrigerating plastic bags, maybe I was unlucky and the gate got slightly damaged?

Poor packaging, but not likely the issue.  I have seen latent failures due to prior partial damage from ESD, but not specifically in IGBTs or power FETs.

Hope your repair and future work goes smoothly.

Or should I just put a box fan next to the primary

I did try running compressed air into the inside turn but it did almost nothing.

Haven't tried compressed air, but it would be difficult to get enough air flow to be effective.  I did add a pair of 120mm fans blowing up at my DRSSTC primary from opposite sides.  Definitely helps, though probably not as much as water cooling would.  Might be sufficient if your mechanical design allows for air flow from below primary.  I added copper shielding over fan motors and initial bit of lead wiring to prevent internal motor electronics from getting confused by primary magnetic field.  (My primary is litz wire, so no reasonable water cooling option.)

If switching spikes are caused by bus inductance dumping energy into parasitic capacitance, wouldn't the amount of overshoot decrease as bus voltage increases?

There are multiple possible causes for spikes.  I'd guess these are caused by diode turn-off (reverse recovery time ending) during post-zero-current switching.  Diode turn-off causes sudden drop in bus current causing sudden rise in voltage due to bus inductance.

This seems to me like not strong enough feedback soon enough. And reducing the CT ratio further might make it better, but I don't want to have too much past 1A of feedback current right?

Depends on power rating of 51 ohm CT burden resistor in your UD2.7 build and intended duty cycle of your coil (max setting of interrupter).  Yes, 1A is a reasonable number.

My full bridge coil starts oscillating at much less voltage.

Half bridges need twice the bus voltage to ring up at the same rate (same output voltage).

Edit:  One more thought:  What type of diodes are you using for feedback CT input clamping (input to comparitor, D1 and D2)?  If using 1N4148 or other non-schottky diodes with higher Vf, that will increase startup voltage and current required to get good phase lead.  Also, what value is your comparitor hysteresis feedback capacitor (C33 in many UD2.7 schematics)?  If using 2.2nF (or anything above ~1nF) that would be another contribution to increased startup voltage and phase lead current.

Would that mean the coil mainly uses the counterpoise and the mains ground is just extra security, or will it transmit interference to the mains no matter what even if the capacitance of the counterpoise is significantly higher than the toroid?

The larger the counterpoise is the less anything else to do with grounding matters.  Modeling the electric field around a Tesla coil including all the building wiring and plumbing and construction materials is too complex to be tractable.  And the location of wiring and plumbing is rarely known either.  That's why there are varied simplified views and opinions.
My goal for inside use is to think of the building more as a low-quality Faraday cage with random wiring and plumbing all around, all "grounded" for the purposes of TC frequencies.  Of course, wire inductance makes the cage far from perfect.  But most of that inductance is common-mode between hot and neutral and safety-ground.  There is very little differential noise introduced.
With any option, your small coil is extremely unlikely to damage any electronics, at least any devices more than a meter or two from coil.  At worst it interferes with radio communication.

Here's the low side switch, 250V ish DC bus voltage. (200ns/div), (Vce 50V/div), (Vge 10v/div)

Thank you for scope settings.  These first three zoomed-in traces look excellent!  Very clean switching with Vce transition occurring at turn-off and turn-on just before zero current.

I also still have significant spikes up to like 500V on the first few cycles! I know this is normal but should they be this high with 250V bus? I'm planning to run 680V bus voltage (1200V IGBTs)

Those spikes do look rather high, though may not be enough to damage anything.  Spike voltage likely scales with current more than with voltage.  Hope you get other responses and opinions too.

I see a snubber cap across top brick Vbus.  Is there another on the bottom brick?  Presuming so, and if other opinions say those spikes are high, a few options come to mind:
1) What CT ratio do you have?  If ratio can be reduced without exceeding UD2.7 feedback burden resistor (51-ohm) power, that will help.  Makes UD2.7 phase lead track sooner (at lower current).
2) Adding a laminated bus bar structure to H-bridge to further reduce stray inductance and allow connection of additional snubber caps.
3) Add R+C snubbers on brick outputs.
4) Make the self-oscillating mod's to UD2.7 driver that I've described in other treads and a couple people have implemented.  When self-oscillation is set to roughly primary frequency, phase lead starts almost immediately.  If you are interested in this option I can find those threads and add links.

If I zoom in on the bridge output ringing on the first cycle, it's about 25MHz. Is this just from bus inductance, or could it be an artifact of poor measuring?

The higher frequency ring is less important and is likely very sensitive to measurement details.  The more important frequency is width of each spike, which looks to be just under 1us, say 900ns.  That half-cycle spike is ~550kHz and not so likely to be a measurement artifact.  It is likely due to inductance, internal to bricks and snubber caps and external connections between bricks and caps.