Is it possible to disable the volume drop when a notification comes in (without jailbreak)? I'm looking for a way to prevent notifications from lowering the volume of music when they come in, as I feel this really distracts from the listening experience.

I would rather not have to turn on Do Not Disturb, but I couldn't find any other setting for this in the Settings app. Is there a way to disable this volume drop without jailbreaking my iPhone?
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.