Yes, I have connected all GND wires together.
I have tried powering both devices from USB (USB -> Espruino Wifi -> external board connected to GND and 3.3V pins of the Espruino Wifi)
and also tried powering both boards from an external 3V power supply (not 3.3V, only 3V...) using the GND and 3.3V. pins of the Espruino Wifi with USB disconnected.
The output in the logic analyser looks the same - when the external board powers up, SCK stops pulling low.