Apple Bluetooth Mouse

Personally, I have the Magic Trackpad for that at home. At work, I sometimes have to temporarily connect an old wired mouse, just to get to the bluetooth menu.

You may try the on/off slider switch at the bottom as a form of retry. But that is only anecdotal.

If your Apple wireless mouse, keyboard, or trackpad isn't working as expected - Apple Support

I find that once my Mac is on the login screen where you input your password, make sure your mouse is fully charged and switched on, and start moving it around. When I do this, my computer seems to sense the movement and suddenly after a few seconds the cursor on screen will start moving too and the mouse is connected. This trick seems to work even when I am logged in and the mouse stops working. I just wait for my computer to go to sleep and then re connect. I hope this works for you too!