No. The service you are logging in to does not hold the keys so they can't be leaked, passkeys do not get reused between services, it's effectively impossible to fall for phishing attacks with passkeys, and it's effectively impossible to fall for scammers trying to get your keys since there isn't any mechanism to directly dump the private keys out.

Pretty much all the problems related to passwords are solved by passkeys, having them synced between your devices does not impact that.