I use Zotero and sync the attachments to my Nextcloud instance via WebDAV. The database is synced to the Zotero servers, because that's the only option. With a bit of care on initial setup for new machines, it works wonderfully. The real value are the PDFs, some of which are of course really hard to get by. And those are "local" in the sense of "local server", yet available to all clients.

There was a forum entry that self-hosting the database is a topic being worked on. That's my number one gripe with Zotero, it just seems weird: if using multiple clients, users have to sync to the Zotero servers, yet the storage space for attachments there is minimal (which is okay; Zotero pricing looks reasonable but of course, own storage via e.g. Nextclodu is much, much cheaper). This basically forces a hybrid solution, with bring-your-own-storage. If all of Zotero's data could be self-hosted, now that would be a streamlined, great experience.

Then again, I am anal about my entries' metadata and often correct faulty data found online. Syncing that to Zotero servers is kind of like giving back? I always thought that data might help improve Zotero's own auto-fill functionalities, which I'd like helping with.