The thing is, even when webrings were a thing, they weren't very good at showing people where they'd go if they clicked. Just because someone liked site1 doesn't mean that they'll like site2. Likewise, joining wasn't necessarily straightforward, so you might volunteer to join your site to the webring, but not be included. Most webrings sent you to the next site in the list instead of giving you a page where you could select the site(s) you wanted to visit.

There were good reasons people stopped clicking webring links and using search instead. Search could be more inclusive as well as more comprehensive.

If you're thinking of redoing webrings, learn some lessons from search. Don't just reproduce the same failed concept.