You'll want to start the Oculus program and Steam, then start AH3, then select use oculus VR. That's how it works with the CV1 and Rift S. I haven't tried it with Quest. Hopefully it works the same way when tethered.
One thing to check, when you are tethered and in the Oculus program, see if AH3 is available from the store. That should show you if you're in the Quest version or the regular version of Oculus. I expect you need to be in the regular Oculus program for AH3 to work.