Calibre-Web has shelves (that can be public or private), and a built-in OPDS server (that you can use from within phone apps such as Moon+ or a rooted Kindle).

Calibre-Web has shelves (that can be public or private), and a built-in OPDS server (that you can use from within phone apps such as Moon+ or a rooted Kindle). It not only replaced Calibre's server for me, but also those few functionalities for which I've previously used Goodreads: organizing books into shelves, marking them as read, keeping track of how many books I read in a year.