For anyone else coming across this thread in future, I tried ALL of the fixes that are out there and none worked. It would unlock my Mac mini about one time in a hundred (and startling me in the process). I left it on despite the 99% failure rate because the newer unlock for system preferences did work about 95% of the time. Go figure.
However, one thing I did which has now got the basic unlock working 90% of the time… was to move the Mac. Quite what the problem was that physical location affected OS unlock but not System Preferences unlock I cannot imagine, but that’s what largely sorted it for me.
It could also be the presence of a brand new M1 MacBook Pro on my desk. Maybe the mini knew it had to toe the line more.