Playing Doom 3 on Windows 11 Pro. I have several other running apps that get repositioned when playing this game in Fullscreen.

I've attempted to switch off 'Fullscreen' and change the resolution (see screenshot). If I don't change the resolution, the graphics suck, but when I do change the resolution, the game starts in Fullscreen.

Solution is to also edit...

set r_windowHeight "1440"
set r_windowWidth "2560"

However, the defaults are changed to upon PC reboot. I saved a backup and can easily Save As, but is there a way to stop this behavior?

Maybe where the game is installed to is somehow write-protected and preventing you from making changes in DoomConfig.cfg? Try re-installing the game outside of system folders like "Program Files (x86)" where it is not protected by the operating system, and then try launching the game with this command-line parameter:

+set r_fullscreen "0"