Hey! This sounds like the issue I had (and still have?), almost to the detail.
Welcome to the nightmare. It's not going to be fun.
I'll share my experiences in case this advises you in any way.
The PC would go to a Black screen under certain GPU loads, and after some amount of time of being on this Black screen, any sound playing will distort and then stop, and then the PC will restart.
During this entire process, the power never cuts out. It never shuts off. It just loses video signal, and then eventually restarts.
This doesn't usually happen when a load is first being put on the GPU (like when a PSU can't meet a sudden power spike). It almost always happens randomly when the PSU was already under some load state.
There would be no BSODs. But there will be an Event ID 18 (on AMD CPU systems at least since I think that Event is exclusive to them?) with a "cache hierarchy" error type. Sometimes a WHEA log. Sometimes a Watch Dog log. The Event ID 18 just says there was a machine check exception (which likely explains the restart, so the CPU is signaling it?), the WHEA is a generic 0x24 error, and the Watch Dog will usually point to the GPU drivers. Specifically,
VIDEO_TDR_TIMEOUT_DETECTED (117), VIDEO_ENGINE_TIMEOUT_DETECTED (141), VIDEO_MINIPORT_BLACK_SCREEN_LIVEDUMP (1b8), and
VIDEO_DXGKRNL_BLACK_SCREEN_LIVEDUMP (1a8) were the ones I'd see for that.
Seems the GPU is getting unstable somehow, the CPU catches it and decides it's a machine check exception condition, can't recover, and signals a restarts.
I also noticed the issue is worse with RAM at stock, and more stable (but still very unstable) with the RAM profile active. For example, League of Legends was one of the light enough games to never crash for me. But then if I disable the RAM profile, it starts crashing as well.
It's a nightmare to resolve; let me tell you that now. I went down a path over two months trying a lot of things, like BIOS updates, different drivers, a ton of random certain settings in both the BIOS and OS (like PCI Express power saving things, ULPS, etc.), certain voltages for the CPU/Infinity Fabric system, a total reinstall of Windows. I swapped CPU and it happened on a 3700X and a 5800X3D. So, not CPU itself. I tried with XMP on and off, as well as removing half the DIMMs. Completely tore my system apart and cleaned and disconnected and reconnected everything, multiple times, and even tried different SATA/PSU cables where I could. Multiple DP/HDMI cables tried. Disconnected fans/storage I didn't need and left the case open. Lots and lots of really minor and niche things I won't even mention but just to say I've got to comical lengths to rule things out. Trying a different motherboard, RAM, and PSU was just about the only things I didn't try. All that stuff was stable with the prior video card, but it's a low power draw video card (GTX 1060 to 7800 XT). The system passes all CPU and RAM stress tests (Prime 95, Memtest86, and all OCCT CPU and RAM tests), but sometimes fails GPU ones (Furmark on its own is usually fine, but the OCCT "GPU variable" in particular, and Furmark plus a browser seem to trip it, so these sorts of scenarios mimick whatever games are doing to cause it). Add to this that a seemingly endless amount of people complaining of Black screen (or Green on HDMI) to restarts on the 7800 XT and I think I had tried enough to rule other things out and figured it was time to suspect the first thing I should have tried all along.
Ended up doing an RMA on the video card and it mostly resolved the issues to begin with (while 23.12.1 and newer drivers introduce more of their own...), but I've had it happen now once on the new one too (started with a new use case so it's possible this one never resolved it so much as made it much more rare?). This time, the game was flickering White for a single frame a few times before it happened. Previously it'd just happen with no symptom beforehand. I'm tempted to try a new PSU if it starts happening more even though I don't think it's a PSU issue (largely because changing the GPU is what changes how bad it is), but I don't know. There's two many "mixed" symtoms. Changing trhe GPU changes the severity, but yet changing RAM profile speeds also does?
So based on what I tried and what you symptoms are (same as mine!), I'd say changing the video card itself is mostly likely to bring change, but it's possible it won't eliminate the issue. PSU would be the next thing to change, but... you changed three. And everyone else I saw with this issue (at least on the 7800 XT) never had success changing the PSU. If it's actually power related, it's either on the GPU itself, or maybe with our homes/outlets.
I don't know if post-pandemic stuff just has poor quality control, like maybe GPUs since then are using poor power regulatory stuff since the issue seems findable with both AMD's and nVidia's last two generations (but more so AMD).
Whole experience has been super frustrating. For
the part that has ballooned in price most of all, it's infuriating to be having such issues.
In any case, good luck. Like you, I just got tired of it. Spending months with nonstop issues and even losing data due to corruption over it breaks you.