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?