A few days ago, French outlet Melty reported that Switch would support Bluetooth headsets based on an interview conducted with Nintendo’s Yoshiaki Koizumi. However, it turns out that information was incorrect.
The site now has a follow-up report in which it states that Bluetooth headsets aren’t actually compatible. There was either an incorrect translation or misunderstanding. Nintendo France passed along the news to Melty.
Of course, this doesn’t mean that Switch doesn’t support headsets at all. You’ll just need to use a wired option.
Thanks to Kenshin0011 for the tip