For me (with iPhone 11 pro, ios 13.1.1/13.1.2, and Airpods 2) -- the only issue with low volume ring/alert is when "looking" at the phone. Otherwise, ring and alert tones are full volume. So for me, this issue is resolved and was just my misunderstanding how "Attention Aware" features work.
However, it seems the behavior is different with other iPhone/iOS/Airpod combinations, including those which don't even have Attention Aware features. So in addition to the discussion here, I encourage everyone still having this issue to send a bug report to Apple using the following form:
https://www.apple.com/feedback/iphone.html
Be sure to include your specific combination of equipment (iphone model, ios version, airpods version) in your bug report, along with a description of the problem and under what conditions it occurs.