That looks like a defective graphics card with the symptom artifacting. It's either the core itself is bust or some of the VRAM modules malfunction.

The issue only happens with this game.
I tried a recent (released less than a week ago) benchmark tool on Steam (Black Myth Wukong) and it ran smooth with no glitch.
I finished Rise of the Tomb Raider two months ago, and it was fine, launched it again yesterday, still fine.

Is it possible for a defective card to run all games perfectly but one?
I will try to find other free demos or benchmark tools, today, to test the card.

It always depends on how the game uses the card. Like you could have ray tracing enabled but in the other games disabled. Or the memory could be stressed in a different way.
You could try to downclock the card. See that the temperatures are good and most importantly open the card to see if the cooling was applied correctly.
In any case you don't have some experimental hardware with poor software support. AMDs 6800XT is well established hardware that should not show such artifacts.

This looks like a problem with VRAM, perhaps one memory die is defective.
Try running Unigine Superposition benchmark in a loop for 30 minutes at 8k preset to see if the GPU is stable.

You can try to reduce the graphics settings from the game launcher to Very High or High. I had issues with Rise of the Tomb Raider and Shadow of the Tomb Raider on Ultra, but reducing texture quality to Very High made the games work with almost no issues at all.

I just ran Superposition Benchmark at 8k and it was stable.

The green artifacts are just present when I launch SotTR, only in the main menu, and just for 0.5 to 2 seconds, until evrything but the menu itself is black. Every time I start a game or a replay, it's just straight black. When I get back to the main menu, it's already black and stays black (the artifacts never come back until I launch the game again).

When I lower the quality (especially anti-aliasing) it just makes the transitory phase with green artifacts last a second or so longer, before it's all black. In-game is still immediatly black, though.

No benchmark seems to make my GPU fail. It only happens in this game.

Try other things like Superposition on everything highest and Cinebench R24 with the new GPU stability bench and especially Furmark to really heat it up.

Since you say that 2D HUD elements are visible, but everything else is black, I suspect the issue is related to shaders. And the way the artefacts appear, it looks like the the shaders that draw an image overlay on top of the whole scene are affected.
What CPU are you using? There is a known issue with some games and 13th and 14th gen Intels CPUs that is triggered by shader compilation.

I ran this game on RX 6600 and RX 6800XT, without major issues on DX 12 (mostly using Steam In-House streaming to another PC). I had to reduce the Texture quality to Very High, or the game would crash. First start after a driver update would take a very long time, otherwise it was fine (except some known issues with DX12).

Other options you can try, if you haven't already:
- Using game launcher, set the graphics to Medium or Low. Set the Resolution to 1920x1080@60Hz and turn on VSync. Disable all settings that apply post processing to the whole scene (motion blur, bloom, screen effects, screen space reflections)
- reset the shader cache at the GPU driver level
- try running the game with the alternate renderer (DX11/ DX12)