The Nintendo Switch does have Bluetooth, and you can use it to connect wireless headphones or controllers.
To sync a Nintendo Switch controller, you'll need to go into the "Change Grip/Order" menu on your console. There, you can add up to eight controllers.
The Nintendo Switch 2 comes with two Joy-Con 2 controllers, plus a Joy-Con 2 Grip and Joy-Con 2 straps. They can be used in numerous configurations, but if you're looking for even more options, there ...