In general I recommend checking protondb.com if you're having issues with any game on linux. Lookup the game and scroll past the steam deck entries. Often somebody has posted a solution there.

I your case, switch to Proton experimental and use these launch options:

eval $( echo "%command%" | sed "s/Launcher/LariLauncher.exe'.*/bin/bg3_dx11.exe'/" )

It switches the game to launch the dx11 version. Alternatively, rename bg3_dx11.exe to bg3.exe or change the game from vulkan to dx11 in the launcher (if that can be done in the launcher). Vulkan is known to crash for some on Linux.

As a sway user, thank you for coming back and posting the solution. ProtonDB is great but not many sway users there and we sometimes run into more unique problems than users running with an actual DE do.