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It didn't originally, but it had a bluetooth transmitter it was using for the joycons and other controllers. A system update in 2021 added bluetooth audio support. The patch noted that not every headset would work, and microphones won't work at all, but it's there. Go to System Settings -> Bluetooth Audio to use it. I haven't had any problems getting stuff to connect, but I've also only tried pairing two things so that's a tiny sample size. One of those has volume control that successfully sends volume up/down commands to the Switch, the other fails to adjust the volume.

The PS5 also uses bluetooth for its controllers, so they could do the same thing if they wanted.