The Nintendo Switch does have Bluetooth, and you can use it to connect wireless headphones or controllers.
The Nintendo Switch 2 is finally available worldwide, we've been playing for a few days (and probably not sleeping enough). One of the things making that easier is that Switch 2 has Bluetooth ...
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.