Just wrapped up my stay. My booking was recognized as a MMS booking and I was welcomed as a MMS Gold(smith?) (I assume because of Globalist). I was offered free breakfast at the restaurant daily as a result and received a welcome note/gift in the form of chocolate covered nuts.

My Hyatt account was automatically credited with qualifying nights and points for my stay, aligned with what I was told ahead of the stay.

All in all a great experience and convenient hotel right next to Copenhagen Central Station.