Fetch one of the black female-to-male+female wires from the second cable set. Connect the female side side of this wire to terminal #4 of your meCoffee.
Remove the gray cable from the steam thermostat and connect it terminal #4 using a black cable from the set. The original gray wire’s purpose is now reduced to connecting the steam button to terminal #4 of your meCoffee.
If your original steam thermostat is still mounted and functional:
Connect the female+male side of the black cable to the upper terminal of your steam button on the side which carries the LIVE signal / has a wire on it. Disconnect the wire which was originally connected to the terminal.
When you press the steam-switch the boiler goes to 100% until it reaches the steam-temperature