This isn’t just a Mastodon problem, all fediverse softwares struggle to keep an accurate tally of faves/likes/whatevers on posts from remote instances
It doesn’t look like this anymore on mastodon.social
Search isn’t free so it’s up to the admins to decide how good/powerful they want their search bar to be.
It shows all followees/followers of a user if said user is local, but if the user is remote, it will only show local followees/followers of that user because knowing what remote accounts follow what remote users also isn’t free.