I have spent several hours investigating this issue, including all the steps mentioned by Heather above. I ended up doing a “repair installation” of Windows (10 in my case), and File History started working. That is until the KB5122878 update was installed, which broke File History again.
I can confirm that uninstalling KB5122878 re-enabled File History on my system.
It’s important to note that even though File History stops working there is no reporting to the logs.
A quick web search confirmed that KB5122878 (windows 10) and KB5124008 (windows 11) are widely reported by users to break or disable the File History feature.
The fix is to uninstall the mentioned update and then pause updates to prevent it from being re-installed on reboot, however Windows is not letting me pause this update for some reason.
Unfortunately, I’ve had several issues with File History over the years, and file backup is far too important a task to leave to chance, so I have begun my search for an alternative backup solution. For those who might be interested, the open source project Kopia seems to be a good candidate.