This question over on Worldbuilding reminded me that I've once read a story that was exactly about a war between Kardashev III civilizations from the perspective of puny Earthlings.
It kicked off with an American electronics shop being offered a contract, by mail, to manufacture gadgets to spec. Payment was in-kind, in the form of mundane electronic components (resistors, capacitors, that sort of thing) which were impossibly high-quality. The gadgets didn't do anything that made sense, and they were to be delivered to a bizarre location (possibly a deserted Pacific island?) so the protagonist got curious and followed a delivery, which was picked up by a flying saucer. The aliens then noticed him poking around and abducted him and his love interest. They were very polite and patient, and explained that there's a war between them and their ancestral enemies, conducted at the scale of entire galaxies. They were hoping to gain a bit of an edge in production capacity by farming out tasks to primitive civilizations that could just barely handle them. Unfortunately, they are losing, and this means that the Earth is probably going to be destroyed. The protagonist saves the Earth with a brilliant strategic insight of some sort, which the aliens were too hidebound to think of.
I read this in an anthology published in the late 1980s or early 1990s, but I am pretty sure it was written in the 50s or 60s; it was definitely set within 25 years of 1950. It was at least novella-length. I can't remember the title of either the story or the anthology, or the author's name, or the name of any of the characters. I think the two K3 civilizations at war were called "Llana" and "Guerra" or something like that.