"Oh, usually my bank just logs me in, that's strange. Let me just go grab my username and password and type it into this site that looks like my bank."

Same thing is going to happen with passkeys for non-technical users for exactly the same reason you stated. People will think the integration is busted and manually copy/paste the non-passkey credentials in. In that way, I would argue that passkey is not stronger protection against phishing attacks unless its the only way to login. It is, at best, a convenience for users.