Indeed it does, I now see. Interesting!

The old one used Bluetooth if you upgraded it during the transition period or you have a Windows box.

I had to borrow a friend's computer to get mine to run in BT mode because I gave up using the Steam Link fairly early and didn't use the controller again until I bought a Deck, by which point the grace period where a system update fixed it had long since expired.

My usecase for the steam controler was limited (robots); I've always used the dongle, and never needed/desired to explore direct bluetooth as an alternative.