It's not a server-side component but something integral to the passkey itself. Everything is on the key and there's no third party - just the key, and the site you're authing to. So when you auth with a passkey, it includes some details around "this came from a Feitian model x or yubico model y or bitwarden or...". That's blank, IIRC, if it's Apple.
And then if a corporate type has said "well we only gave our employees Yubikey 3s", they can instruct their idp to only accept passkeys for Yubikey 3s.
This is a tradeoff - their employees can't register legitimate, useful personal passkeys like their phone, but an arbitrary (not dedicated nationstate) attacker is a bit less likely to somehow takeover the account and add a Feitian key. That mismatch is a nice signal to block the user.
But in general, outside of corporate identities, no one has any interest in caring what kind of passkey you use. GitHub doesn't, certainly, outside of resident key requirements, a different bundle of fish.
(and yes, Dan is definitely great at this stuff, read his blog on this stuff).