Oh! And for those who don't know:
Nintendo Switch 4.0 Adds Wireless USB Headset Support
https://www.youtube.com/watch?v=PBLB_NkBxto
https://www.reddit.com/r/NintendoSwitch/comments/77dc85/400_update_added_support_for_wireless_usb/
It seems that it works wonders with the Playstation headset. Also, you can have it in undocked mode with a USB-C to USB adaptor.