I know that this would probably require a complete server overhaul, and users can already use discord or other third-party programs to contact another player.

However, I have personally experienced the issue of trying to contact somebody in a full lobby
through a third-party program, but they don't respond/don't notice I've messaged them.
This could be a good implementation in TBN though, since it's still in development, and I believe servers have not yet been established in TBN

Now, as I said, this would be a tedious implementation for TB and easier for TBN, but it's just a suggestion after all, right?

Well, all they need to do this is what something like games like Robocraft use. Where you can have group chats, and clan chats, Over watch and many games like this use this. It is just a global chat, which would be good for a game like Toribash honestly, but not just a global chat you can talk to anyone in game with, would probably be too hectic. However, no it wouldn't be an overhaul for them to add something like this, it would just be the trouble of adding it.

Either way, since TBN servers haven't been established yet (to my understanding), it would be easier for group chats like that to be implemented in TBN rather than TB