One identity across products, nothing more than that. No password: a link emailed to you is the only credential, every time. Signing in doesn't change what any product remembers unless you separately turn storage on for it; anonymous use stays exactly as private as it is today.
or
This browser is now recognized wherever you're signed in. Nothing about what a product remembers changes from this alone; storage opt-in is a separate, per-product setting.
A passkey is a faster way back in on this device: no email, no link to wait for, and nothing about it is held by us beyond a public key that's useless on its own. Nothing third-party is ever involved, not Google, not Apple.
Checking your link.