Connect to a Minecraft server.

I’m looking to create an app players can open, type in their Minecraft IGN, it connects to the Minecraft server, and starts playing environmental sounds using Unity’s sound engine based on where the player is in-game. Fading in/out, reverb zones, etc.

All I really need to know is how to transfer data from a Minecraft server to a Unity app/game. Strings, ints, etc. What would be the best way to do that?

This is kinda off topic as this question is purely about the specific application level protocol that a different game (minecraft) is using. The next issue is that minecraft has so many different versions and one of the main reasons why you can not connect to server with a wrong game version are the differences in the protocol. The MC classic protocol is documented over here which was extremely simple. The Java edition (1.16.5) protocol version 754 is documented over here. The Bedrock edition protocol is documented over here.

Keep in mind that newer versions of the game has grown by several orders of magnitude when compared to the classic protocol.

Interfacing with such a server / protocol has nothing to do with Unity. Before you can even communicate with the server you have to complete the login and authentication process. So when you want to interface with a MC server you have to understand the basic structure and concept how the server is built and how it operates. As I said, this is not a Unity related question. From a technical point of view all you need is a .NET TCPClient. You have to take care of the application level protocol yourself.

You may be better off searching for a ready-to-use implementation for C#. Over here there seems to be a quite extensive list of libraries related to MC for all kinds of different languages and purposes.