isn't a mixte the type of step-through that has a pair of stay-sized tubes instead of a top tube, which run all the way from the head tube past the seat tube down between the seatstays and chainstays?
Yes.
Which makes me wonder, is there a name for the half marathon step through which has a single tube from headtube to seat tube supported by a pair of stays from that junction to the dropouts?
Google image search on demi-mixte brings up a load of full mixte frames and this one weird Motobecane where the lateral tube splits part way between head tube and seat tube. Semi-mixte does better
Yes.
Which makes me wonder, is there a name for the half marathon step through which has a single tube from headtube to seat tube supported by a pair of stays from that junction to the dropouts?