Because federation is not universal or instant, you cannot always find users you search for, but in general if you search for a fediverse/activitypub user by fu

Because federation is not universal or instant, you cannot always find users you search for, but in general if you search for a fediverse/activitypub user by full handle on any server, you'll find them. That isn't what tools like these solve for, though - they're helping you make the connection between a Twitter user and a Mastodon user.