You can already do this with `write` which is in most linux distro's. Make sure `mesg` is set to y then test with `echo "hello" | write <username>`. `Wall` messages all logged in users and I wouldn't recommend that approach.

You could try a script that receives notifications and then prints them inside the status bar.

Tmux has refresh interval so you could easily setup a script that prints the notification for a while and then clears it.

set -g status-right "#[fg=colour010]#(/path/to/your/script)#[fg=colour255]"

You could use "wall", but that is not limited to a status bar and just prints in the terminal.