You star! Thank you very much, an updated version of SQLite was indeed the cause. I downgraded to 3.44 and the original configuration came back and backups have been able to proceed again.
I skim the FreeBSD subreddit every few days but completely missed that post you linked to, which is the exact problem here. Naturally I don’t read every changelog when doing my monthly pkg upgrade either.
It doesn’t look like this issue has been raised in the GH issue tracker, I’ll submit something there.
The other important lesson I’ve learned is to make sure I’ve at least got regular snapshots of the duplicati databases.