Instead of using server messages (because they don’t persist when someone joins), add a timer at the top of the screen which displays how long there is until the next competition begins.
The server messages can still stay to alert people when it’s about to start.
When a competition is in progess, just make it display “Competition in progress” and not the time remaining because the time remaining is already stated (unless you want to move that there too, I suppose).
If that “Ability to disable competitions” suggestion makes it into the game, the timer should either disappear entirely or just say “You have disabled competitions” or something like that.