There's a thing called GNUSocial, which I think is open source and federated. No idea if it's popular, I've never heard of it before someone mentioned it on HN a few days ago. https://gnu.io/
Great thing about software like GNUSocial is that organizations can run their own social infrastructure, a bit like how organizations could previously run their own email or any other service infrastructure, rather than rely on a third-party company to dispatch it on your behalf.
By organizations, I'm talking about business, government agencies, educational institutions, et cetera.