Can't connect Espruino Web IDE to Puck using Web Bluetooth

Am I right in thinking I have to disconnect from Web Bluetooth and pair with the system OS to get HID to work as expected?

Yes - the OS will need to connect to the device when it's advertising that it's a HID device. Hopefully @François's Chrome changes will make sure that you can program it even when it's connected - but it'll be a while before they land.

In the mean time, if you need to do debugging you can connect via USB TTL converter and send Serial1.setConsole(true) to force the REPL to stay on USB even when you're connected via Bluetooth.