Matt, I’m damned if I can find it, but this has been previously described here in the forum, is a known bug when using encrypted databases and TimeMachine on a network drive with Catalina (apparently only that combination, IIRC).
What is strange is that I had understood that encrypted databases are automatically excluded from backup whilst open (to avoid the behaviour you describe). That appears not to be the case.
Possible workaround: manually exclude your databases from the TM backup (I don’t know whether that helps, try and see…; if so: set DT to automatically make a daily copy of your databases (it makes a copy and zips it, IIRC) to a location which is backed up.) I believe the next maintenance release will contain a workaround.
This thread contains some further details.