I haven't thought about it in years... but is Delicious still a thing? I would think (hope?) there would be an open source, PHP-based project I could throw onto commodity hosting to collect and manage bookmarks. If this doesn't exist it should -- and I wonder how hard it would be to also integrate saving/sharing tab-sets as well.

There's a whole community of "shaarlist" in France, you can also fuse several shaarli in a "river"... Some rivers are my 2nd HckrNws when I want to read something.