> think with passkey you don't own the private key. It's in your device and managed by the OS. That's one of the reasons I don't use passkeys (the other being that if I lose the device I can't access my account)

It is not true. You can move passkeys between OSs if you have a password manager or an OS that has this ability. For example, I store my Passkeys in iCloud Keychain and I have them synced on all my Apple devices.

There are cases though, where the website can force the requirement of a device bound passkey, but that is something it is not very likely you will encounter.