When I open the game, whether through the launcher directly or through the shortcut, it opens to just before the main menu and crashes. I haven't touched the game in several months, but the only thing I could possibly think of being the issue, that I already tried fixing, is that when I re-organized my HDD where it was installed to be less chaotic I messed up the file locations in some way, but even after I reinstalled on my SSD it still doesn't work. Other than that, I haven't done anything to change the files as far as I'm aware.

I'd try deleting the configuration data that are located in the Windows registry HKEY_CURRENT_USER\Software\Crystal Dynamics\Tomb Raider\. Beware: editing the Windows registry can harm your system. For security reasons, before doing this, I strongly suggest to make a backup of the whole registry or create a restore point.

TR1 GOTY is crashing after startup. It is typical problem for epicgames edition of GOTY, and it seems, for GOG version too. Due this, I guess, gog version is identical as epicgames version.

Tomb Raider 2013 is unable to run fine on newer graphics cards (RX 6xxx and similar). I have a RX 6600 card, no chance with epic, steam or gog edition - simply no chance.
The only two ways are:
a) to force to use DX9 instead DX11 - start regedit.exe, find the "Tomb Raider/Graphics/" directory, a change "RenderAPI" from "0" to "9", or
b) to use the "Reshade" utility - bypassing the render in the game. A bit difficult, but the best solution.