It might be helpful if you could give some actual examples of apps which are showing this behavior. On my Nothing Phone (3), I am an avif Audible and Spotify user, I also regularly listen to my MP3 with the MissingCore Music app - never encountered any issue with audio stopped to play when an app gets moved to the background. Also Audible and Prime Video keep downloading my stuff while being in the background.
There are some apps which obviously are designed to stop when minimized: YouTube for example or playing a video / audio on Discord.
At this point I could only guess there is some kind of battery setting which might be the culprit here. Go to settings, battery and disable any energy saving modes, disable intelligent battery for now and also go to each app's properties and check if they have background running enabled.
Do you have any 3rd party battery observation or optimization apps installed?
Does it happen when listening via headphones (BT / wired), right on the phone or both?