Also with your suggestion I quoted above, a far better approach would be for us to address that in dialogue. Let our character talk to someone and tell them whether or not we had a house.
Pillars of Eternity1 had a great opening like that - we were able there to define our background further, and reasons to coming to the new setting. Most of it was flavour and player expression, but some of it got reactivity further down the line.
I don't think it would be impossible for Larian to have a house reserved for PC in each district of the city - assigned based on background - maybe required to be bought if player picks an Origin and is not from BG.
However, the issue I see that we have not one, but 4 players. If 4 players in coop make a custom character with noble background, that would potentially mean 4 seperate mansions for 4 characters. That could be silly.
Or of course, house might not exist as such, and camp visuals might change depending on our background - not exiting but logical. But than agian - whole background if we have more than one player.
