So it looks like the Nintendo Switch does have bluetooth capabilities (the switch uses bluetooth in order to communicate back and forth between its joycon wireless controllers). There is one important factor though that looks unfortunate for your question regarding your wireless earbuds and the Switch - it doesn't natively allow bluetooth headphones to connect to the system.
There however is a workaround for this that many people may not even be aware of. The Nintendo Switch's 4.0.0 update/patch seemingly now allows wireless usb headsets to connect. You still can't connect wireless earbuds/headset natively to the Switch, but you can apparently do so by using a USB dongle.
You will either plug this wireless USB headset dongle into the dock or the switch handheld (depending on how you are playing at the time).
Some verified bluetooth headsets that work on the Switch are:
Creative Sound Blaster Tactic3D Rage
Creative Wireless HS-1200
Logitech G930
Logitech G933
Logitech H800
LucidSound LS30 (with optical cable plugged into wireless dongle)
LucidSound LS40 (Requires optical cable plugged into wireless dongle)
PDP Legendary Sound of Justice
Plantronics Audio 510
PlayStation Gold Wireless Stereo Headset
PlayStation Platinum Wireless Headset
PlayStation 3 Wireless Headset
Skullcandy PLYR 1
SteelSeries Arctis 7 (with 3.5 mm 3-pole cable)
Steelseries Siberia 800
Steelseries Siberia 840
Turtle Beach Ear Force P11
Turtle Beach Ear Force PX3
Turtle Beach Ear Force Stealth 450
Turtle Beach Ear Force Stealth 500P
Turtle Beach Ear Force Stealth 700
It is important to note that while the switch does have bluetooth and the 4.0.0 patch/update did allow this to work with bluetooth headsets and dongles, since this is not official hardware being sold, a further patch on the Switch could potentially cause this to stop working. Just be aware of this before moving forward and buying yourself any of the listed bluetooth headsets above. Hope that helps clarify things, let me know if you have any questions!
