Does a Windows Digital Signature and a PGP signature perform the same function?
Well, yes and no. The windows digital signature you refer to is present because Windows requires all executables to be signed. Otherwise Windows will complain that the executable is from an untrusted publisher and Defender SmartScreen will block it. Windows uses it to verify the ...
OpenPGP doesn't produce a raw Ed2519 signature. It includes additional data about what was signed, the hash that was used to pre-hash the data, the key that was used to sign it, and other information. For example, if you use gpg --list-packets on the signature file, you get this:
# off=0 ctb=a3 tag=8 hlen=1 plen=0 indeterminate
:compressed packet: algo=1
Don't reinvent the wheel. Unless it's broken... which it is not.
There are plenty of tried-and-true authentication methods that don't involve the transmission of private keys, which should ALWAYS stay with the user. I would recommend against using PGP call-response as outlined by @ThoriumBR as the main authentication ...
While this would theoretically be possible, the common tools do not support it. PGP has --export-session-key and GnuPG has --show-session-key & --override-session-key, but the latter is only used for decryption. For encryption, a new random session key is generated every time.
Display the session key used for one message. See