I’m not trying to complicate the issue by mentioning another mobile OS, but it sounds like the behavior I noticed on my Android. If this doesn’t sound like what you’re experiencing, disregard. I have no Apple products to help test.
I play music, another alert happens (Nav alert, Radar Detector, etc) and Plexamp would pause and resume after the alert was finished. If the alert lasted too long, then Plexamp would pause and remain paused. On other music apps, the volume would dim, for lack of a better term. I asked the developer of my RadarDetector app what he used for sending his alert and he referred to “ducking” which might be only an Android thing. This behaivor was noticed on version 3.1.1 and was fixed on version 3.2.0.
My forum post: https://forums.plex.tv/t/plexamp-and-audio-alerts/
I mention all of this because maybe Apple has something similar to ducking, and perhaps a Plexamp Person can chime in and let you know if this is something to look forward to on Carplay.