This project implements a reproducible example of how to record and play audio with a Bluetooth headset even if the app is in background.
The difficulty is to receive button presses from the headset, especially the pause command. With the current implementations the button press is not detected. But these events would be crucial to implement start and stop recording via the buttons presses.
The implementation starts the AudioEngine, and therefore the recording, immediately. If audio data is actually processed is managed separately. This allows to initiate the recording even from the background via a headset button press because the recording is already running and only the virtual recording is started. Actually starting the AudioEngine when the app is in the background is not possible (see this StackOverflow answer).
Because the AudioEngine is running all the time, only the pause command could be emitted. But this event is not detected. The problem here is to find a way to receive this pause command from the headset button.