bookshelf 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.
Cloudflare offers an API, which can be used to update the records. It’s as good as a DDNS.
Have you tried playing the files locally with VLC or MPV? Is the audio out of sync in the files themselves or is it because of Jellyfin?
Sometimes the audio on my client is out of sync, but after stopping and resuming the video, the audio syncs again.
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.