One thing of importance is that unless you are signed in most servers will not fetch remote things (like profiles) that are not already cached. Really threw me for a loop thinking I broke stuff when I couldn't find my bridged profile on remote servers.

Also, posts in search are generally just what's already known to the server AFAIK. Way to many servers to try to query them all, though as long as your signed in searches for users does work across the fediverse.