Proton crashes and cannot be uninstalled

When I try to run any application with Proton I get

/media/motofckr9k/EffolenaMKIII/SteamLibrary/steamapps/common/Proton 5.0/dist/bin/wine: error while loading shared libraries: libwine.so.1: cannot open shared object file: No such file or directory

When I tried to reinstall Proton, I noticed that the uninstall function inside of Steam does not work. Even if I delete Proton it doesn't uninstall. The path shown in the error message is correct.
Other applications are not affected (I can uninstall other applications via Steam).
This issue happens with all Proton version on my system: 5.0, 4.2, 4.11, 3.7 and 3.16
Verifying data also doesn't help.

I am on Steam August 27 2020 00:28:19.
This is running on Linux Mint 19.3 (Ubuntu 18.04.3)

It worked just a month ago.

EDIT: After tinkering around with it and rebooting the machine, it doesn't throw that error anymore. It does seem to have some other problem accessing the device though:

35.656:0028:002c:err:shell:SHGetFolderPathAndSubDirW Failed to create directory L"C:\\users\\steamuser\\Local Settings\\History".

There is tons of errors like these. Feels like a permission issue, but checking those folders, permissions are fine. I can create directories with nemo and mkdir.

No source file or test is named. Start by reproducing the failure with Proton 5.0 on Linux Mint 19.3/Ubuntu 18.04.3, checking the reported libwine.so.1 error and Steam uninstall behavior. Done means identifying a reproducible cause and verifying that Proton runs and can be uninstalled.