go to sleep and turn off the computer screen ?

The screen should turn off before the computer automatically sleeps.

Any Keyboard & Mouse activity will prevent automatic sleep.

Some applications can prevent automatic sleep.

1) As a test:

What happens when you select Sleep from the Apple dropdown and refrain for touching the mouse or keyboard...?

2) Check your Lock Screen & Energy settings.

Set Turn display off when inactive to 10 minutes.

Turn off "Prevent automatic sleeping when display is off"

Test with the screensaver set to never and display off timer set to 5 or 10 minutes.

I have a Mac Mini M4 and have the following when inactive for a given set time:

and this:

I don't sleep the Mini because so many users have reported problems with sleeping. And since the drive is solid-state it doesn't need sleeping.

You can sleep your Mini as den.thed discussed and if you run into problems with sleeping you can try my settings.