Allow watch to unlock your Mac

Make sure that you are using two-factory authentication, and then if you hold down the Option key when choosing the Apple Menu, /System Information, select Wi-Fi in the sidebar, then look for Auto Unlock: Supported on the right side. See this support document for additional information. How to unlock your Mac with your Apple Watch - Apple Support

I've had some troubles with mine in the last couple of days. I have Catalina version 10.15.4 on a 2019 MacBook Air. I turned it off, then shut down the MacBook. I the powered the MacBook again, then went in and started to set it up again. This time I made sure that my Watch screen was unlocked before I set it up, and was still unlocked when I clicked on OK after entering the password. I worked on the computer for a bit, then had to take a phone call. When I got back and clicked on the mouse, it unlocked with the Watch.