Thank you for the detailed testing and for sharing reports from other users.
Based on the reports so far, this does appear to be a File History regression related to recent Windows updates. KB5101684 specifically included changes to File History, although Microsoft currently lists no known File History issue for this update.
Since similar behavior is now also being reported after Windows 10 KB5120249, I recommend submitting the issue through Feedback Hub so Microsoft can correlate the reports and investigate it.
For now, reselecting the same backup drive in Control Panel > File History > Select drive may serve as a temporary workaround.
Hopefully Microsoft can address this in an upcoming cumulative update.