Cannot edit restored backup plan
In the end, there didn't seem to be an answer to this issue. It was likely caused by an import of a very old configuration file from my previous machine.
I deleted all the backup plans and made new ones. The existing backups were successfully connected to for the plans which used legacy file backup - the backups continued where they had left off. The one backup that I had set to use the new (non-legacy) file backup format wanted to backup all files again.