Password managers and/or operating systems can manage private keys just fine. websites shouldn't be concerned with how the keys are managed, or be able to make demands on how users store credentials, or know device details for users.
One thing I dislike even with systems like FIDO2 is that the websites/apps can block list your FIDO key's vendors. Similar trends suck. Passkeys are just one iteration in a long line of systems designed with corporate interests in mind.
The system validating the authentication needs only to verify that the credentials are correct. If users want to use TPMs, HSMs,etc.. or none at all, that's up to them. And no information, other than what is strictly required to verify the credential should be transmitted over the network. a signature of challenge data from the app should be sufficient. the user's public key shouldn't be signed at all by hardware, a trusted 3rd party,etc.. the registration process should take care of establishing public key trust to the authenticator/app. The whole thing feels insidious.