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5 months agobookshelf looks like something you’d like. It doesn’t seem to automatically index the files, but it does work without Calibre and has no UI. It only supports Epub though.
I don’t know if it saves progress and I can’t test it right now.
With EteSync you can share calendars and tasks. Apps like Tasks.org can communicate with EteSync (on Android at least, i don’t know how the support is on iOS). The devs also provide a (Web UI, which can also be self-hosted.
The main feature of EteSync is end-to-end encryption, you can also self-host it.