I've tried both 3dfx and DirectX and if I skip the intro movie the game stops responding. If I wait for it to finish, I can get to the main menu and play the game, no problem. I'm on Windows 11.

Mine doesn't do this for the intro, but did do it for the first cinematic after starting a new game. I don't have a resolution for that other than letting it finish, but would love to hear one in case I have the problem again.

This happened to me too. I couldn't even close the game, had to log off Windows to quit it.

I found a solution that works for me.
1. Install the game from GOG.
2. Install DirectX 11 renderer: moddb.com/mods/unreal-directx11-renderer-for-ut-ug-rune-and-dx/downloads/directx11-renderer-for-wotrune-hp12-c bu-and-ds9tf-version-162
3. Install Quicktime Fix. Simply copy the files to the "System" folder: community.pcgamingwiki.com/files/file/655-directdraw-patched-quicktime-4/
4. I still have the high-resolution textures installed. But this is not necessary to play. moddb.com/mods/the-wheel-of-time-esrgan-pack
5. The videos will be played in a smaller window at the top left and can be skipped with ESC.
I'm totally happy! :-)
I have 4k resolution and perfect brightness.

Since posting the links doesn't work, I had to remove http and www in the links.

Installing this totally fixed it. Kinda sad the FMVs have to play in a small window, but at least the game's playable.