It's expected that you won't see the Puck in the system menu because it doesn't offer anything (like a keyboard/mouse) that the system is interested in. The auto-connect thing is very strange though - I can't think of any reason it would do that.
Can you:
Close the Chrome Window with the Web IDE (and check that there aren't any more windows open that might be trying to use Web Bluetooth)
Check that you don't have any other applications running that might be trying to connect (if there's some Hudl 2 software, it's possible it got confused and tried to connect to the Puck?)
Disconnect from the Puck via the Bluetooth window
Take the battery out of the puck for 5 seconds and re-insert it
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It's expected that you won't see the Puck in the system menu because it doesn't offer anything (like a keyboard/mouse) that the system is interested in. The auto-connect thing is very strange though - I can't think of any reason it would do that.
Can you: