How does Google Password Manager sync your passkeys then?
EDIT: Private key is not transmitted off of your device when authenticating, but it can be transmitted off of your device by your password manager.
"The difference between passkeys and passwords is that passkeys are cryptographic key pairs. The key pair is specific to a website. One half is shared with the website, and the other half is private and stored on your device or in your password manager." [0]
"Passkeys are securely backed up and synced between your Android devices" [0]
"Passkeys are stored in your Google Account..." [0]
"Your iCloud Keychain stores and syncs them [passkeys] between iOS, iPadOS, and macOS devices." [0]
[0] https://support.google.com/chrome/answer/13168025