I'd be surprised if it matters. In older TLS versions (the version is not specified either) the suite might include various handshake parameters, but they're irrelevant after the handshake completes anyway. After that, regardless of version, realistically you are doing AES or maybe ChaCha20. There are lots of options in TLS 1.2 and earlier, but you won't use any of them, since both machines know AES.

The fact it's bottlenecked somewhere but CPU is fine suggests some configuration parameter somewhere results in not as much data being in flight for HTTPS, limiting throughput over this very fast connection. If so, fixing this parameter would make the noticeable difference essentially vanish.