Bluetooth Mouse Not working after Factory Reset !!

MacBook Air 2020 m1: macOS Monterey 12.2.1

Mouse Model: rechargeable goojodoq m05 2020

it worked normally before I did delete all MacOS settings (erase MacBook & factory reset)

after that the mouse show its connected (with red light) but there is nothing showing in macOS bluetooth device also the mouse not working (I think its still connecting with the old MacOS system that I delete)

there is no reset button on the mouse (maybe the mouse save the bluetooth name or Mac to link directly), because as soon as I turn on Bluetooth on the Mac, the mouse color changes from green to red directly, meaning that the connection has been successful

any one have idea how to solve the problem ?