Or website curators all agree on a /webring.txt file (similar to a robots.txt) where they list websites they think are similar?

An important part of what made webrings good, though, was that they were curated (some more than others, but still...)

Having sites just list others the site owners think are similar is just the site providing a list of links to "friend sites" -- which also used to be a common thing. That's also fun and useful, but not what webrings are about.

I'm not sure I see the difference in curation between a webring and a "other cool sites" list, except that in the webring case there needs to be a central curator across several sites, so it's effectively just a single person's "other cool sites" list spread across several sites.

"Other cool sites" lists were quite popular back then. That's what I used for site discovery instead of webrings.

The best webrings were curated by topic rather than just being a list of sites the ringmaster likes.

Links to friend sites - does this have a name?

As a way of discovering content, I love the idea.

Or... or.... a little banner that says, "From around the Web:"!