(Re)Posting this here as after many hours of searching the Internet I only found this answer once in Larian’s forums. Hopefully google indexes this one better.

If, as me, you were still having issues launching BG3 after Hotfix 4 Patch 11, this was my solution:

For anyone who needs it:

This issue - in a lot of cases - seems to be related to leftover Patch .pak files from before Patch 4.

- Navigate to your Baldur's Gate 3 Install Folder's "Data" folder.
- Find every .pak starting with "Patch" or "Patch_"
- Delete them.
- Restart Baldur's Gate 3.

With Patch 4, most of the pre-existing patches are now referenced in the PsoCache file. Deleting the Patch .pak's themselves seems to solve the invisible character/missing main menu button issue.
This has been a confirmed fix for many Nvidia users, and a multitude of AMD users.

Source:

https://forums.larian.com/ubbthreads.php?ubb=showflat&Number=920265#Post920265

Also, as protonDB mentions, you should be using some of the latest proton-GE builds with hotfix patches (depending on when you read this post).