Thank you for the question OP, I am researching the same.
I'm not finding in the documentation provided that RECORDING can continue in background. It only suggest that PLAYBACK can continue when an app moves to the background (inactive, paused, hidden lifecycle state). Although please let me know if I am missing it in this resource!
(https://developer.apple.com/documentation/AVFoundation/configuring-your-app-for-media-playback)
Based on the specific activities that the documentation says 3rd party iOS apps CAN do in the background, it excludes audio recording. This concurs with all the stackoverflow, reddit, etc. questions & experiences for iOS 14-ish and later that I've found... But I haven't found any actual Apple documentation that says "no, this is not possible for 3rd party apps".
https://developer.apple.com/documentation/uikit/preparing-your-ui-to-run-in-the-background
Topic:
Media Technologies
SubTopic:
Audio