iMac no longer recognizes the same wireless mouse

Dig out, barrow, buy an inexpensive USB mouse and use it to troubleshooting your wireless mouse connection.

see "Setup up earlier Apple wireless input devices" at > Set up your Magic Keyboard, Magic Mouse, or Magic Trackpad with your Mac - Apple Support

Did you use it with another device? If so, you may need to forget it on that device before it will pair with another.

You're welcome.