I can only comment on my experience searching for communities in lemmy and people to follow on mastadon, but in both cases I am not sure I'd say "works quite well" would describe my experience.
But also that's not what I think OP was talking about.
They want a search engine for a random fact like google. It's been long true that you need to add "reddit" to the end of any google search to find the info you needed.
I can only comment on my experience searching for communities in lemmy and people to follow on mastadon, but in both cases I am not sure I’d say “works quite well” would describe my experience.
Lemmy search works pretty well on larger servers, and they're indexed by major web search engines.
The microblog side of things is worse, with Mastodon long having near-useless search because it might "encourage negative social dynamics" or some such. Some other software, such as Akkoma has had better search, and Mastodon has recently improved somewhat for accounts that opt into being searchable. Mastodon directs search engines not to index most pages.
Some people get very upset about attempts to build general-purpose fediverse search tools.
I think it's a small, but very loud minority who have unrealistic expectations about how other people will use data they share in a manner that's inherently rather public. I kind of see where they're coming from, but ActivityPub with open federation doesn't work that way.
There are various websites that catalog all the instances they can find, but I can't remember the one I used back in the day an don't know if they search communities too or just instances