I guess you are using Capacitor.
I’m running into the same issue as you and it looks like the last error about ‘no background task exists’ has something to do with Capacitor’s BackgroundTask Plugin, wether you’re using it or not (BackgroundTask.swift)
It’s clear something changed between iOS 12 and iOS 13, but so far haven’t figured out how to define the required entitlements for background audio.
EDIT: It only happens when using HTML5 Audio.