Have a look at https://owntracks.org/ . Has apps for android and ios and you can self-host the server component

I was getting super excited until I saw the turn based combat

1. stop refreshing the front page/inserting new posts automatically
2. mark as read on scroll past
3. multireddit
4. decent ipad app - mlem is a rgeat start on iphone but no ipad support
5. consistent 'go back' experience - I have on a number of occasions gone into a post then clicked browser back button only to be presented with a completely different list of posts on my front page

I have airsonic running in a docker container behing Nginx Proxy Manager. I use play:Sub on my iphone and it lets me download albums to my cache.