Magic Mouse not working

My Bluetooth Magic Mouse, which has faithfully served me for a dozen years, stopped working on my MacBook Pro two days ago.

As it was old, I assumed it had run its time and purchased a new Magic Mouse.  This is not working either, in just the same way.

Both old and new Magic Mouses (Mice?) show as connected to the Mac in System Preferences – Bluetooth when connected to the Mac by a Lightning cable and turned on, the new with a charge of 3% and the old with a charge with 0%, even though I have charged them well past these levels.  But when I take either off the Lightning cable, the connection fails and the mouse does not move the cursor.

I have tried everything I can think of, in every combination:

-      Un-pairing the mouse, turning it off, turning off Bluetooth and restarting the computer in Safe Mode and then restarting the computer normally.

-      Resetting Bluetooth (by typing “sudo pkill bluetoothd” and my password in Terminal) and restarting computer in Safe Mode and then restarting the computer normally.

-      Reinstating the Mac OS (I was on Sonoma 14.4.1 and that is what has been reinstalled)

I have just arrived in a charming but Apple Store light Central Asian country for two weeks and would really like to be able to use a mouse.  It surely is not a hardware issue as the computer (regularly) tells me that the mouse is connected to the Mac.  So this should be fixable by me if I can be told what to do.  Please can someone help.