Your other post about this was about an iPad also not recognizing the mouse. If neither the Mac nor the iPad can be made to connect to the mouse, then, there may be a problem with the mouse.
One problem could be that the mouse is paired with another device. In that case, you must unpair it before using it with another Mac (or iPad).
If you managed to get it working with the iPad, then you would need unpair it from the iPad in order to use it with the Mac.
Also, in the image you posted, the mouse is switched off. Of course, it would need to be switched on for it to pair and work with another device.