koreader is an open source ebook reader application originally designed to replace the firmware on Kobo E-Ink reading tablets, and then ported to run on Amazon Kindle, Android, PocketBook, and Remarkable devices. Under Android it runs as a normal application. It also runs as an application in Linux and (reportedly) in MacOS. It reads basically all non-DRM book formats. It is highly configurable and featureful, though not infinitely so.
If you have an OPDS-speaking book server, it can search and download from that. If you want to run a tiny sync server for keeping track of which page you are on across multiple koreaders, that’s pretty easy.
If it ran smoothly on MacOS and I could get it to work on my semi-antiquated Chromebook, it would be even closer to perfect. Sadly, it doesn’t – yet.