F-Droid is an installable catalogue of FOSS (Free and Open Source Software) applications for the Android platform. The client makes it easy to browse, install, and keep track of updates on your device.
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I bought Moon Reader Pro a million years ago cheep on sale, and it has been great. Still love it, but I like to check out open source readers every once in a while.
Lately I have been using Librera FD. This open source version on f-droid unfortunately has the network features (sync/opds) disabled. The play store version has those enabled. The interface is a bit unusual, but it's a powerful and flexible reader.
On f-droid, KOReader is the absolute best. It's got every feature you can imagine which can be overwhelming but empowering. It has a couple of littlebugss here and there but if you're wanting FOSS and a feature rich reader you can't beat it.
Cloud account? Probably not an option with most FOSS tools. I suppose you can syncthing the koreader directory which is where save state and other stuff is located.
I use KOReader and it has a built in page syncing. You register within the app and save the positions; then you login on another device, copy the same file (for example I use the built in cloud connection to access Nextcloid/Dropbox and download the book) open the same file and it is synced.
Librera has a Dropbox integration (possibly in the pro version) and it may sync. But I never used such features since I prefer KOReader on ereader.
A simple one i like is booky mcbookface but it doesnt really meet your requirements. I have tried librareaader but find it complicated to use as a casual user
It may be a little hard to find a FOSS app with a cloud backup, I like to track my progress independently through BookWyrm, you may know it, it would be the federated version of Goodreads.
Librera is the ol' reliable in terms of FOSS document readers, some people may find the UI a little clumsy tho, but it probably is the most feature-rich you will find.
Personally, being a minimalist myself I like the simpler Book Reader. Search, index menu, dark mode and page persistence, it has all I need, nothing more, nothing less :)
Koreader or librera
Aldiko saves your progress in epubs you are reading. I use Calibre to organize various collections.
Haven't seen one that uses a cloud service.
Not FOSS, but Lithium on the play store has what you need and the app is free of tracking and ads.
I find open-source apps in this department to be still lacking.
It is not possible to make free open source app without tracking to save in the cloud.
"Book Reader" from f-droid has "sync folder" option, but I never tested it. I guess of you sync that folder with some other app (like syncthing, or google drive) you can have it in other places.