MacBook Air Won't Connect to Logitech M720 after connecting to another Logitech Mouse

I have the weirdest problem with my MacBook Air M3. I would pair my mouse at home (Logitech M720) and all will work fine. However, I have another mouse at work (Logitech bluetooth mouse as well but a different model). The work mouse would always connect just fine. But I've notice if I connect to the work mouse, the laptop would not recognize my M720 at home anymore. I would have to forget the device in bluetooth and repair.

This is consistent. I can take the laptop out of the house and back and the home M720 would connect just fine. Until I bring the laptop to work and pair with the work mouse.

Any idea how to debug this?