Function extract_public 

pub fn extract_public(
    path: &Path,
    out: Option<&Path>,
) -> Result<(), GitwayError>

Extracts the public key from a private-key file and writes it to out.

If out is None, the public key is written to <path>.pub. Passphrase handling: if the private key is encrypted, passphrase must be supplied. Public-key extraction does not strictly require decryption (the public part is stored alongside the private), so an unencrypted .pub is still produced.

Errors

Returns GitwayError on I/O or parsing failure.