I don't have an Android so can't verify this, but CNET makes it sound like the app scans automatically:
> If Tracker Detect notices an AirTag that's been following you for at least 10 minutes, the app will then allow you to play a sound from the AirTag so that you can more easily find the physical tracker. [1]
I use Android and tested the official app. It doesn't warn you. You need to open the app and perform a manual scan.
There's an open source app called AirGuard that runs/scans in the background and sends you a notification if they detect "tracking". It drains some battery, but works okay.
But.. shouldn't BLE receiver be completely passive? I mean, it isn't transmitting anything, which should pretty much limit the algorithm to "get list of MACs, compare to another list of MACs, sleep 30s".