OK so I just setup a blank controller (version 8.2.93, latest stable), no UI account (you just click "Advanced setup" and then skip when it tries to get you to supply an account), I then adopted a factory reset UniFi AP AC HD I had laying around, it accepted it without complaints, and automatically updated it to the latest firmware available (this is an option that's on by default in the controller software).
I then factory reset the AP AC HD again, and set it up as a standalone AP using the Android app on a freshly reset Pixel 6 running the latest version of Graphene OS.
Both methods worked fine to setup the AP without any UI accounts involved.
This is available on all APs able to run the current version of the AP firmware, which is literally all the APs released since and including the AP AC Lite (which is from 2014 or thereabouts, they support their devices for a very long period).
7 Pro Max is the current top-end model.
I highly recommend setting up a controller for managing the AP though, even if you don't keep it running 24/7 (you can simply start it on any PC whenever you want to make configuration changes), as when they're in standalone mode a lot of the cool features don't work, you only get one SSID (per radio) and no roaming support for example, whereas when managed by the controller you can have up to 8 SSIDs per radio on the latest APs, you can access telemetry, setup roaming, etc.