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".