You have in effect made your own repeater.

So the next step for you if you already have a 'client-bridge' is to get a router and hook the client bridge to the wan port. It gets very complex because of how the encryption keys work. Next only some repeaters can change the SSID.

It makes it easier to control who has access. First the apartment complex must support WDS which is many times not turned on. The reason extender repeater do not work is for a couple reasons. This would be use to connect to a ethernet based device that does not have a wifi card. If you actually have the range extender I would first see if it has a option to run in client-bridge mode. These type of devices have a history of massive security exploits. It means everyone else on the same wifi can see each other equipment. Still I would never connect devices like that to a more or less public wifi system. It will request a connection on the 2.4g radio band. Since the device only has a 2.4g radio it does not even know the 5g signal exists.

Wifi extender spectrum