It doesn't try to solve the same use cases that Calibre does, but I built an open source (EPUB only) manager / reader / statistics tracker called AnthoLume [0]. It mostly stemmed from me reading in KOReader [1] on my Kindle, and not having the ability to sync the progress to my iPhone / iPad.
It's got metadata matching, support for multiple users, and statistics tracking which allows me to have a "Leaderboard" that shows how fast you read (words per minute). Fun competition between my wife and I (that I'm 100% losing). It's a Progressive Web App and utilizes a Service Worker to support 100% offline reading as well.
There's a demo server [2] (creds are "demo" for both user & pass).