Nintendo Switch - Joy con doesn't work in 2 player mode?

If I want to play a game in 2 player mode (e.g. Mario Kart) then I can't connect the right Joy Con. As much as I press ZR / ZL, the controller simply does not connect, but the right Joy Con does con works but whether it is on the console or not it works perfectly only it does not connect in 2 player mode.

What can I do there?

Do I need a new Joy con?

Are the ZR / ZL buttons broken on the Joycon?