Jellyfin via Finamp satisfies the first but I don’t think the second. I haven’t confirmed but I’m doubtful. But maybe someone reads this and doesn’t care about the second part and it helps them.

If anyone gives Finamp a try on iOS, get the TestFlight version. The one on the App Store is a fair bit behind. They’re testing a new UI but only on TestFlight and it’s a huge improvement imo.