I self-host xBrowserSync. It’s a bookmark sync tool, not a link manager, but it does that very well (set-and-forget - it’s almost invisible). There are browser extensions and mobile apps
I’ve also used Shaarli, which is more of a link sharing tool. Don’t remember much about it, though - sorry.
I self-host forgejo. I’m not a heavy or advanced user, and it suits my needs. I barely use github any more: mainly to star repos I like, and find and use repos (there’s a ton there - it’s almost ubiquitous).