The fastest way of getting court attention--as suggested in the article--is most certainly through a reasonable accommodation claim.
I think a key to the apartment is something that's de facto supplied with a lease. They can't require you to spend additional money for a smartphone and service. (They key can be a fob or card in 2022, of course.)
I'm really surprised that this hasn't been settled. It seems unjust that you can surround a piece of public land--or someone else's land--with your private land and deny access to it.
I remember Disney was successfully sued to allow access for the Hilton Orlando Bonnet Creek resort because Disney owned all the land that would provide access to it and didn't want to allow it.