I'm looking for recommendations. I usually use Overdrive with books I've downloaded (I think in the epub format). But now I hear that Overdrive is no longer being supported (I think the company wants people to use their Libby app instead). I'm hoping to find something open source and privacy minded. Also not wild about what Overdrive is doing to public libraries
Librarian here. Yea, Overdrive's near monopoly has been concerning for awhile, though libraries will en-mass drop it if they start selling user data. It's still safe from that currently.
If you’ve got a kindle, the kindle app will sync which page you’re on between devices. Plus you can just throw any ePub at it and it will appear on all devices.
I use Kindle and Hoopla to read borrowed library books. On iPad I use MapleRead, which is my definite favorite app because it allows a lot more choice in terms of density. I do most of my reading on Android because my ereader is Android and it's just better than LCD/OLED for reading, and I use MoonReader there. I don't love it compared to MapleRead, but after a lot of experimentation it's the least bad I found on Android.
I'll also add scribd. It's a subscription service, and discoverability kind of sucks balls, but the library is OK and I usually find 20-30 books a month on there to read that aren't available from my library.
I use an old 4th Gen kindle from 2011. Amazon has a web service where you email a file to a specific address and it is added to your library. Alternatively I have used calibre to load ebooks via USB.
If you're on Android, I'm a fan of Moon Reader (+ version to support dev). It'll cover pretty much any reading file including comics. That's if you already have the files.
Local library is probably the best and safest route for getting ebooks. There are libraries online that archive books as part of their mission statement. Legality is grey, but there's also archive.org and project gutenberg for books outside of copyright.
I use Moon+ Reader. It's not open source but it's so snappy; page changes are instant and scrolling is flawless. It connects to my calibre server too. Android only I think.