Unify APs not showing up

If you are using the supervised HA I believe there’s a Unifi Controller add-on - not something I’ve had experience with though.
If you are using HA container you can run the Unifi Network Controller in a docker container (or natively installed on a suitable environment) separately.
The above options will give you the ability to use the Unifi Network integration without additional hardware (unless you want to).

Alternatively you may be able to use multiple instances of the Unifi Direct integration but it may get messy to manage IMHO.

I’m using the dedicated Unifi hardware controller at home (just moved from Cloud Key Gen2+ to UDR) but run a full Unifi network and camera setup.
On my employer’s office HA setup we use the Unifi network controller installed on the same NUC that runs HA container.