Under FIDO, to which Google declares compliance for passkeys[^1], the private key should never leave the client device so they shouldn’t be stored on the server… but that applies to the service provider (e.g. Shopify website). Identity provider, in this case Google or Apple, of course do store private keys on their servers for backup purposes, only they declare them to be encrypted by the sync passphrase.
I guess there are two workflows here: one under normal usage scenarios, one under TAO[^2] or other “law enforcement love letter” scenarios.
Granted that identity like Google provider controls all data flows for any software keys, from storage (Android), sync passphrase entry (Android) to operating system and application updates (especially after hosted developer keys were introduced to Android[^3]), it would be naive to have any illusions that under TAO scenario they won’t retrieve that one way or another.
This shouldn’t be the case with hardware authenticators, of course, which are also allowed by Passkeys. Or at least building a side channel for private key retrieval will be much more difficult even in TAO scenario.
[^1]: https://developers.google.com/identity/passkeys
[^2]: https://en.wikipedia.org/wiki/Tailored_Access_Operations
[^3]: https://www.theregister.com/2021/07/01/android_app_bundle/