The IndieWeb is “a community of independent & personal websites”, as stated on the IndieWeb homepage website. That makes it both something one can use for themselves, like I do at my website or something people work around in a shared, federated way like how micro.blog, indieweb.xyz and other projects in the space work. In fact, it tends to be more communal since it’s up to people who are also using it to define how things work.
Right now, that’s a bit more tricky for people to do with ActivityPub software like Mastodon or Pixelfed (which isn’t a fault of those projects - it helped them grow and be used a lot) but I have seen others do it with things like microblog.pub and the like.
If there’s a political undertone to take, one could say that any form of federation that isn’t user-local makes them a form of digital feudalism (which is good or bad, depending on your relationship with people and land). The IndieWeb does have a more self-liberty-driven vanguard, but I’ve seen newer folks come to nudge that in a different direction. I would even go as far as to say that the IndieWeb wants YOU to have the final say over what you do with what you have, versus needing to wait for some random software changes or protocol update to enable it.
Happy to edit/correct anything.