I had an issue with my Apple Watch series 2 and my iMac where the iMac suddenly stopped unlocking while I wore my Watch. I think to fix it, I had to repair the Watch to my iPhone. Maybe try this?
I always found this feature to be hit or miss, like a lot of Apple's features lately. When it works, it is great. When it doesn't it is a real pain because the total time to unlock the computer is multiplied significantly.
I turned it off. I just leave the mac unlocked at home. If someone steals the mini they would have to turn it off and get a login anyways. I guess it would be useful in an office.
While you’re wearing Apple Watch, your Mac can sense when you’re nearby and automatically log you in. You can also use Apple Watch to approve other requests for your administrator password.