It's interesting sitting here on an old version of #Calckey seeing someone on #Mastodon server telling their fellow user that posting to unlisted will opt-out of #search when I can see Unlisted posts in my antennas quite easily though I believe this has been rightly rectified in the newest versions of [#Firefish / #Iceshrimp but need to confirm]. Being hidden from the Explore tab on Mastodon is not the same as being unsearchable across the fediverse. Frankly, there's little understanding even among admins across the #fediverse about what's a Mastodon / Mastodon API function that is federated to other Mastodon servers but doesn't translate well outside of Mastodon on other #ActivityPub connected platforms like #Misskey and it's forks, #Hubzilla and #Friendica, or rapidly growing platforms like #Lemmy and #Kbin. Kbin also scrapes posts from across the fediverse and puts them into its own magazines.
Unfortunately simple, up-to-date documentation doesn't really exist to explain the realities of federation vs what your admin said was the reality. AP was not built with privacy in mind, and 'security through obscurity' was mostly a Mastodon thing from when folks thought either the Mastoverse was almost the dark web, or the whole fediverse [which has never been the case], and Google et al weren't interested in scraping it.
Unfortunately we have a cadre of devs across all fedi platforms who'll give glowing lip-service to both the fedi and ActivityPub histories of being built by queer or other minority identities but still won't work on giving folks the granular #privacy and #safety controls that weren't included in those protocols, and whose feature roadmaps now just look like bird site 2.0 funded by the milquetoast liberals in political tech who provide their seed money.
Beyond Mastodon and GoToSocial, every other fediverse project treats posting to public as opting in to search and indexing. Indeed, this is pretty much how the ActivityPub protocol handles such too.