It's more like co-owning. Both the owner and the HOA own the property. But at least with my HOA the agreement is they handle everything outside my walls, I handle everything inside.
Depends who owns it / who payed to have it constructed. If the tenets own it and payed to have it constructed, or payed someone who payed someone... Then it's a condo or a co-op depending on whether you own a unit in the building or own x% of the building which entitles you to a unit.
If another organization, almost always some form of government, payed to have it constructed and owns it then it is public housing.
If it's anything like cities skylines original, houses just pop up according to demand with seemingly no construction cost calculated, probably because it would add a ton more complexity with mortgages and speculative markets etc. for little gain to players who mostly just want to play with trains and metros.
I would have preferred to have it solvable through policy or something. A giant business, with high earning employees would of course raise the average rent if not regulated. I find it rather amusing, that it actually happened in the game as well without being explicitly build in.
Making people in society feel like they own nothing and are getting milked by those few who do own everything is a good way to see things break down, it's happening real time, we're watching it right now in the US.