I don't think the fediverse has this, but I'm a bit confused why so many of these comments are puzzled at why you would want it. We have fediverse twitter, fediverse insta, fediverse reddit, fediverse discord, etc -- why not fediverse facebook/myspace/carrd? Where users could just have small personal (or corporate) pages about themselves that aren't as blog/news focused on the main(user) page.
I don't even think it would be a huge stretch to implement: a big focus on user page customization with a small microblog interface taking up a portion of the screen would do it. (Disclaimer: not saying easy to create, just not that far out of reach vs everything else the fediverse has).