With a Bluetooth audio device connected—be it a pair of wireless headphones, earbuds, or a speaker—the Switch is only able to wirelessly connect to up two controllers at a time.
The console also doesn’t support the microphone on wireless headphones or speakers, presumably because voice chat functionality on the Switch is already reliant on a smartphone app, and Nintendo warns that gamers may experience audio latency depending on the type of Bluetooth audio device being used.