Sounds like you want to put your Mac to sleep with a delay that allows you to turn off your mouse. Not sure why, if your Mac is asleep then your mouse will use almost no power.
The keyboard methods for sleep apply to built-in keyboards (my MBP has one, and they work on that but NOT on a connected Magic Keyboard), so if you have the Mac Mini in your byline then these options will not be helpful.
Sleep, log out, and shut down shortcuts
Alternatively, you can use the Shortcuts app to create a simple shortcut with two commands, Wait (set the delay you want) and Sleep, and you can assign a keyboard shortcut to it.
Intro to Shortcuts on Mac - Apple Support
