Calibre-web isn’t Calibre. It uses the same database, but that’s about it, unless you use the optional conversion mod on the linuxserver container.

A docker container is preferred, but again, CW isn't Calibre. Same database but completely different management system + also lacking a lot of the sync opportunities.

The issue is that there's no open protocol for library syncing. It doesn't exist because all big players (Amazon, Kobo/Rakuten, B&N, etc.) have their own proprietary system, and need no open alternatives.

OPDS is a thing but it's meant to replicate a physical library (one you can walk into) in behaviour and approach, not a personal library (list all books I have and give me easy access to them). It's essentially just an RSS-style feed that has no defined structure, thus isn't software navigable - e.g. there's no guarantee you can list all book series, or all authors, and most implementations usually give you very roughly defined "recently added", or "hot now" book lists...

I've actually been working on a solution for this, something that provides an almost Kindle library experience (see all your books from a remote server, sync down the remote ebook file, sync back read progress, filter/search based on book properties, etc.), while being flexible enough for non-readers applications as well. But I haven't even gotten to the point where I can define the API contract properly, let alone the backing database and mapping to Calibre. Honestly at this stage I feel like the best approach is starting from scratch, establishing modern requirements, and going from there.