I use Time Machine for backup of my Macbook at home. The backup target I use is a simple two drive Synology NAS (I also have other backups in place). Overall this has worked great for me. However, since the recent MacOS Tahoe update I have begun having issues with Time Machine not being able to perform backups.
After some quick searching, I found the solution.
The first step is debugging. Apple is known for providing a polished experience, but this also comes with some drawbacks, namely verbosity.
I found this this post by Chipster which listed the following debug command:
log stream --style syslog --predicate 'senderImagePath contains[cd] "TimeMachine"' --info
This provided the much needed verbosity.
The error I got was BACKUP_FAILED_DISCONNECTED_DISK_IMAGE which, after some more searching, seemed to be a common issue for SMB attached Time Machine backups. A fix that was suggested by karel250 was this one which seems to fix my issue. So simply just remove any strange characters from the Disk images drive of the Disk Utility, or replace them with NFD compatible characters. The root cause of this, as listed in the discussion thread, is that Time Machine moved from using NFC to using NFD encoding for Unicode characters.