I used to use xbrowsersync [0] for cross-browser sync and rn I'm using raindrop [1]. Xbrowsersync is self-hostable, but raindrop is not. Both are FOSS.
ive been using floccus for a few months now and its been working ok so far.
it syncs to the webdav server on my synology but there's also the option to sync it using decsync (which is sort of like a local webdav server for each device) and some other sync service like syncthing or dropbox to sync the files.
floccus has an android app or it can also be installed as a normal extension with the kiwi browser.
i tried xbrowsersync first but i had some issue when i used it with vivaldi where a new copy of my bookmarks showed up in the "deleted bookmarks" section every time a sync happened, and i couldn't see any way of fixing that either which is why i went with floccus in the end
I run a simple little docker container (found the image on github)[1] to host the webdav server myself, since I don't run Nextcloud or anything else that exposes webdav. It works quite well for me.
