That's really a solved problem. As an example, Google manages to have a web version of Youtube that works on iOS mobile Safari adequately. (It's not perfect but it works.)

There doesn't seem to be anything snowflake special the Patreon iOS app needs to do that a web app cannot handle.

Does it support playing media even when it’s backgrounded? Stuff like Picture in Picture?

Yep. It works with Democracy Now!'s web player.

So Patreon will need to become a reader app like Spotify/Kindle then that can do all this offline but you cannot subscribe or pay in the app.

The problem is that Patreon wouldn't even be able to tell people they can donate to their creators elsewhere due to Apple's assinine anti-steering provisions

This is honestly the main problem I have with that. You can argue that in-app purchase brings convenience etc. etc. and Apple deserves a cut and so on. But this enforced secrecy makes users unaware of the cost - they can't actually decide if the cut is worth the convenience or not. Apple relies on people not knowing the cost of the fees and that feels very dodgy.