I don't know why you think this is a huge misuse of the word when many very reputable military historians describe the best of a bunch of shit options as "The merciful choice".
Anthony Beevor quite literally refers to Franco not executing political prisoners but making them live the rest of their lives in prison as "A rare show of mercy", despite obviously the latter option being still absolutely awful. I don't even agree with Beevor in this regard, there's other options here like, how about not jailing political opponents at all.
But mercy is a term that is very commonly use in military history deciphering war planners doing something bad rather than something much much worse.
This thread is moving off-topic but I think one additional point that makes 'mercy' misleading is that the US would have derived an enormous benefit from the use of the atomic weapons and that would have surely been the primary deciding factor in the decision they took. Had they decided to go another route to bring about Japan's surrender there may have been more Japanese casualties but there would also have been many allied casualties and loss of materiel along with huge costs and strains on logistics.
With the examples given there is little cost to the person in the dominant position. There would have been no real detriment to Franco if he had ordered them killed, in fact it would probably have been the easier/safer option so there could be seen to be some mercy in that decision but I don't think it applies well to the US/Japan situation.