I don’t think it’s true for the hardware token. The initial registration sends information about the token to the website (but the website can tell the browser it doesn’t need it, IIRC).
This attestation is meant to allow the service to verify that you use a "blessed" security key with certain security properties (e.g. only a YubiKey 5 they verified to be secure and not some random $5 key with broken RNG off Amazon).
FIDO2 is designed to maximize security for the majority of users, and the majority of users are using Yubikeys or other hardware-backed tokens provided by big players in their space.