I am aware of people saying they see great results with the paid search engine “kagi”. Do you use any other better ways to query the fediverse?
Kagi has a search lens for "Fediverse Forums", which AFAICT builds a list of Threadiverse instances and searches them.
There isn't a great way to replicate that on other search engines, but most of the communities exist on a relatively-small number of instances, and if you're willing to settle for an incomplete search, you might do all right with a site: search that includes the major Threadiverse instances.
Note that a number of Threadiverse hosts have shifted to disallowing anonymous access, due to heavy load from webspiders being run by people scraping content for AI, making them unusable which probably means that search engines aren't indexing them either. It looks like piefed.social is back to providing anonymous access, which I believe it had off for a while, but fedia.io, the main Mbin instance, still has anonymous access off.
https://lemmyverse.net/instances has a list of instances "smart-sorted", which puts the major ones up top.
The top ones are lemmy.world, sh.itjust.works, lemmy.ml, lemmy.dbzer0.com, lemmy.zip, lemmy.ca, programming.dev, feddit.org, sopuli.xyz,, and beehaw.org.
Google supports Boolean search operators, so to search for tigers, search for:
site:lemmy.world OR site:sh.itjust.works OR site:lemmy.ml OR site:lemmy.dbzer0.com OR site:lemmy.zip OR site:lemmy.ca OR site:programming.dev OR site:feddit.org OR site:sopuli.xyz OR site:beehaw.org tiger
EDIT: Also note that while I don't use the Lemmy Web UI's search engine, instances won't see posts unless at least one user is subscribed to the community in question, so if you want to use that search engine, you might have more luck searching on lemmy.world, which is the largest Threadiverse host and most likely to have seen a given post than mander.xyz's, your home instance's.
If you're using the Instance Assistant for Lemmy & Kbin in Firefox, it adds a link to the right sidebar on remote instances to view the current given post on your home instance, which might be useful if you're doing that.