What's wrong with just connecting to mini over VNC? You can even firewall it off and tunnel VNC connection over SSH, or tailscale / zerotier.

I dont think there is any single action you cant perform on Mini remoty. Once it's unlocked that is.

Maybe actions like "Please enter your AppleID", or a popup showing on your physical screen saying "system has to restart now", which doesn't show in VNC. In any case, you don't want this in a server because these are usually used over SSH and those types of popup will simply not be seen. Also, servers are usually administrated using scripting and those popups wouldn't work anyway.