You’re now running into this problem, because you have no Thread hub in your new home: Smart lock pro 4 always unavailable in Apple Home - #5 by Juergen
What at least is proven by your “experiment” is, that pairing with the Nuki lock in principle works. If it does not work in a home with an existing Thread hub, something must be wrong with the Home and/or it’s components. Most likely the Smart Lock can not connect to the Thread network. You might try to turn of all other Thread components that are active nodes so that the Smart Lock has to connect to the HomePod minis Thread radio (Make sure the HomePod is not more than 10m away from the lock).