Where exactly does that first spent joule go, thermodynamically speaking? Is it also converted to heat within the electromechanicals of the heat pump?

Yes so not only are you capturing heat from the environment you are turning electricity into heat in the compressor, both are delivered as heat to the interior. This is an advantage compared to cooling where you must reject both the interior heat and the heat of compression.

To add to the other answer, if you calculate the absolute limit on performance for heating and cooling using the Carnot cycle, the 'heating' case is always going to be '1' higher than the cooling case, because you also get to use the 'work' heat.