Does make sense utilize TLS and Noise Protocol in the same application?
Using two transport protocols is not a good idea. You would double-encrypt your data. However, the symmetric ciphers are generally rather secure if applied correctly.

Besides double encrypting your data you would also get: double the security warnings to react to, double key management, double the initial handshake processing, double the latency.

If you want to encrypt twice it is probably better to perform additional end-to-end encryption / decryption on top of the point-to-point encryption that the TLS security offers. That way you can keep your messages secure over multiple point-to-point connections and after receiving them at the end points. For this you could device your own protocol or you could use web-security.

Generally it is better to perform encryption well once, instead of performing it badly twice. Bullet-proofing your TLS connection makes the most sense if you just require transport protocol security. Encrypting things twice should not be your goal. The goal is simply to secure your messages to the best of your ability.



The noise protocol seems to be in draft stage. Besides that, it seems a rather generic sum of possible algorithms more than an actual protocol. It seems that it mainly has been setup to explain the security behind WhatsApp rather than to be a protocol that you should consider. Just the formatting of the messages is already ill-defined, and it is unclear which kind of authentication method you should be using.