I just noticed that both com.plexapp.plugins.library.db and com.plexapp.plugins.library.blobs.db were owned by root/root. Changing that to nobody/users at least allowed the database migration script to start running.
I am having the exact same problem. Plex (lscr.io/linuxserver/plex) was running fine until I ran an update last night. The docker log just shows the same error you received. I used ChuckPA's Plex DB Repair tool and my database passed all the checks but that did not solve the problem. I will try to downgrade versions of the docker.