If something goes wrong, go to OS bluetooth settings and unpair camera there! Then refresh page and start from step 1.

Step 1: start bluetooth pairing on the camera

Menu → wireless settings → bluetooth → pairing

Step 2: pair camera in OS bluetooth settings

Regular pairing from Web Buetooth is not supported but it is required by the camera.

Step 3: create Web Bluetooth connection

Step 4: handshake

or

Step 5: some actions

Shooting

Playback

WiFi (will disconnect bluetooth)
Power
Device info Doesn't actually require a handshake.