I agree it was an unusual interaction, which is why I mentioned it. We ate breakfast between 8:00am and 9:30am every morning of our stay. We were well within the serving window when we arrived (I had confirmed hours and whether a reservation was necessary the day prior) and they were still seating people as we were eating our meal, so I am not entirely sure what the issue was that one morning - I wonder if they might have assumed we were not guests at the hotel. Every meal after that, they recognized us and knew our room number for the check without me providing it.

Edited to add: The restaurant/hotel website indicates that hotel guests have priority for breakfast, but when we visited over the New Year holiday period only guests could access the restaurant for breakfast. I am not sure if this is the norm or not.