Lemmy instances won't search outside of their own databases if you're not logged in.
But if you are, what it does can be recreated on a command-line by doing:
curl --header 'accept: application/json' https://nerdica.net/.well-known/webfinger?resource=acct:[email protected] | jq .
This shows that your profile is at https://nerdica.net/profile/nate0. Lemmy puts all users at a /u/, but using webfinger means that other fediverse accounts don't have to follow the same structure. For lemmy.world, you're at https://lemmy.world/u/[email protected] in the same way that a mastodon user is at e.g https://lemmy.world/u/[email protected].
edit: ~~However if you webfinger your mostr.pub account, you get: {"error":"Invalid host"}
so any ActivityPub instances will only ever be able to find you if you've interacted with them in some way to get a database entry. Edit: also, I tried to do this again, thought I'd try the npub1 account as well, but got Gateway Timeouts, so there's a bit of jankiness going on too.~~
I know for sure that Lemmy won't, it's likely the same for Mastodon.
I was wrong about not being able to WebFinger your account - I still had the @ at the beginning when I trying. Doing it properly:
gets the right response.
However, I'm logged into lemmy.world and it still couldn't get your account. At a guess, it's because there's a 20 character limit on usernames.