I still mourn the loss of Google Reader.
There are plenty of RSS reader apps, but there are very few with good cross-device sync - let alone self-hosted cross-device sync.
I don't think you could self-host Google Reader, so it sort of feels like these two sentences don't hang together.
Self-hosted FreshRSS + NetNewsWire, works like a charm.
miniflux is pretty good. news.mystuff.net is pretty sweet.
I've been using Feedly ever since the death of Google Reader. If you ignore all the ai bullshit it's simple to use and I've had no issues with cross-device sync.
I've been using one of the numerous "RSS to Email" programs for the past 20 years.
To me that's peak usability, I can use my mail workflow to have cross-device state, I can use my mail clients tagging and spam support to filter, and I have a reasonably good searching facility too.
Some sites only include "teasers" rather than full posts, but they're a minority.