I used to use floccus and the thing I really liked is you can selectively share bookmark groups. So if you have certain links you want everywhere you can do that, but some sets you might only want in in specific browsers. I do not know if the others that have this.
Stopped using it because of unresolvable problems and not much Dev attention but looks like its picked up again so I plan to get back to it.
It is also worth noting that Firefox Sync is end-to-end encrypted. So the amount of data the server gets is quite minimal. (This is unlike the sync of a lot of other major browsers.) So unless you want to hide your IP and activity times from the host self-hosting isn't critical.
If you can selfhost, you can try my SyncMarks AddOn. It will work on any webextension compatible browser, e.g Firefox, Chrome, Chromium, Edge, Brave, Kiwi and so on. You can sync across all Browsers.
The backend is working with selfhosted PHP/MySQL (or SQLITE) stack. If you can't use this, you can fallback to WebDAV as backend, but with limited functionality.
The addon can work together with the standard sync mechanisms in all these browsers, but it's up to you if you want that.
If the addon is not installed, you can access the backend url with any browser and use it as WebApp. With apps like Tasker or HTTPShortcuts, you can share any url, from any to the backend.
There's xbrowsersync which can be used with a self hosted service. I am currently hosting another one for myself, LinkDing. It has import from browsers via html, but no real sync. There's an addon to add new bookmarks directly to it. Another addon, injector is whay made me switch. My search results may contain a previously bookmarked link, this is added and highlighted then.
I am running a cloudron server for me and my friends and thought linkwarden might be available for it but it dont.
I gave xbrowsersync a try and thats exactly what I am looking for. I use it with FF Plugin now and it event auto tags the links. Thanks a lot!