Inside the "Edit" tab of every class there is now (as of 28th March 2022) a "Manage teams" button. When you click this, you see a pop-up that looks something like the one in the image above.
This pop-up allows you to define teams for TEAM COMPETITIONS :)
When you go to set a Competition for your class, you'll now be asked to choose a "Competition mode", which means choosing between individuals or teams.
Here's how the competition teams settings work: