Moving user account manually
You could make a different account on the Mac Mini, and if you right-click on the account you created in System Preferences you get an advanced settings pane and could set the home directory to be whatever you want - ie. it could just pick up the one on the USB drive. You'd then be using your old account just like it was before, running from the external enclosure. Be warned - if that enclosed is missing when you log in macOS will create a new one in /Users on your internal drive.

However, in general, all the users settings you care about are in Library in your user's home. So, if you created a new account, and just copied Library over, you'd get the settings you care about. Then could use the docs/data on the remove drive. It wouldn't need your full drive structure - could move those docs to wherever you wanted.