Not exactly. The remote host, which you have forwarded your agent to, tries to log onto your production host using your public key, and when the production hos

Not exactly. The remote host, which you have forwarded your agent to, tries to log onto your production host using your public key, and when the production host sends it a signing challenge to prove it has the authority of your private key, it can simply ask your ssh agent to do that signing. Once that is complete, you are logged in and the session has a session key that has nothing to do with your pub/private keys. The ssh agent does not do decryption, it just gets the session started.