I doubt re-flashing will help anything here, so I suggest you to forget that at least for now. Especially if you are not familiar with flashing at all.

To me it sounds that your phone is working correctly. (That is, as intended, which might be something else that you would expect, though...)

If I recall correctly, SMS etc. sounds will follow "System sounds" volume, when some media playback is going on. So go to "Settings" -> "Sounds and vibration" menu and try to increase "System sounds" and try if it helps!

Of course, it will increase some other system sounds in different use cases as well, which might be somewhat annoying sometimes, but that's the best you can do without starting to mess around with Resource Policy configuration files, I'm afraid.