2 Apple Watches listed in"Use Apple Watch to unlock apps and your Mac"

I got a new Apple Watch Series 6 on Sunday morning, 

but there is something wrong on my Macbook.

The macOS is now Big Sur (11.0.1)

Apple menu  > System Preferences, then click Security & Privacy.

support.apple.com

I've already done reset my old Apple Watch Series 4 to trade in.

There is not Series 4 on my device list.

I have another Macbook Air that I've never used for a long time, but the macOS is Mojave so auto unlock feature is available. Maybe because of the MacBook?

I called Apple to solve the problem. Though they can't guide me to sign out of my Apple ID, instead they can only guide me to initialize my Mac.

support.apple.com

I can sign out of my Apple ID from my MacBook, but they cannot support for that.

Erasing my Mac is very cumbersome and then requires considerable time to restore from backups, etc.

I am sure that this issue relates to Apple ID. It's not my fault. Well....