Is it possible to disable the volume drop when a notification comes in (without jailbreak)?
Put your phone into silent mode.

When your phone is set to ‘silent,’ notifications will no longer disrupt your listening experience, and will still come in as banners and vibrate your phone.
If you also want to stop vibrations, open Settings → Sounds &amp; Haptics and disable Vibrate on Silent.
Note that on older phones (iPhone 6 and older, including SE) have a preference area labelled Sounds instead of Sound and Haptics.