Mac mini sleep mode settings when connected with Samsung monitor

Personally I never sleep my Mac. I simply use Lock Screen. After a short time the signal to the monitor will turn off and you just need to set up the monitor so that it turns off the display after a set period of time without a signal (many monitors do this by default).

When at idle, the new MacMinis use very little power so sleep is really no longer needed.

Also, with Lock Screen, your mMac is just the way you left it ready to go with no delay.

Here are the settings I use for my Mini and it's monitor:

Set the top two to what works for you best. The other should be set to "Never" as indicated.

Not sure what your issue is but do not use sleep function as it causes too many issues. Just have display turn off after a set time.