Really excited about this!
The only BLE device I have around me is a Sphero BB-8, and the test page I use doesn't show any Bluetooth devices when I try to connect. Not sure where things are breaking down.
I'll try another BLE device later (a BBQ thermometer) and see if I have any luck.
One thing that might help diagnose what's going on: is there a way to enable Safari Remote Debugging inside the browser, so I could see if there's a Web Bluetooth error being thrown somewhere?