Mouse no longer working

The first thing that comes to mind is that the battery may need to be recharged. Connect it to your Mac with the charging cable it came with. Make sure that the Mac remains "on" for the charge to occur. Then buy an inexpensive wired mouse to use when necessary.

Sorry for your frustration. Yes, some of the older mice had batteries that needed to be changed, and were not rechargeable. You could upgrade to one of those which can be recharged, or get a wired mouse as I suggested. I personally have never been interested in wireless mice because of issues like yours. A Mac will work just fine with most any mouse.

I would try using a set of standard batteries instead of rechargeable.

Then if that doesn't work, I would replace the mouse with a new wireless or USB mouse.

I also support what Ronasara say's, most any Apple or Generic mouse Bluetooth or USB will work with a Mac.