I confirmed with my team that we use a raw TCP socket for the port I am trying to connect to. This source on the internet says that:
“The browser is a tightly locked down environment. The only socket connection that you can open from JavaScript is WebSocket.”
This source tells us that WebSocket clients cannot connect to TCP servers without the use of an external module as a middleman.
So the final answer is:
It is impossible for your UXP plugin to connect as a client to a server with a raw TCP socket using the provided modules. It might be possible if you download an external module.
I would love to be wrong about this, if anyone wants to prove it!