This is not my most original post ever. My mouse died on an HP Envy last night, when devicemngr in Windows said all was Ok. Replaced the mouse, which did not come with a Bluetooth. Still did not work. Had to find another mouse (at Best Buy) cheaper, that came with the right bluetooth. Now works.
Actually, in my case, there may be another factor. I had Geek Squad replace the harddrive (after copying the data) six months ago because of occasional crashes and forced restarts due to hard disk errors on the original computer. That stopped the crashes. But the HP firmware updates stopped running. It's likely that one of those vendor-specified firmware updates would have allowed the original Bluetooth (from HP) to accept the new mouse. Nobody thought of that. So that's another way a problem like this can happen. If you have a mystery problem, consider the maintenance you have already had done for other issues.
Update: Dec, 18
Curiously, after the install of the new bluetooth and mouse, HP firmware updates suddenly resumed., with "Pointing Drawing, 5-link micro dongle" whatever that is. (The dongle is apparently the mouse). So this is apparently an overdue update for W10 to make Bluetooth devices work properly.