The culprit was an extra build action (among ~20) that had been cut-and-pasted from Stack Overflow 1.5 years ago and worked splendidly, until an unrelated update (dev machine prerequisite, installed organization-wide) caused it to behave differently on local builds but not on the build servers. The check-in comment of the commit in question was "merge hmm", and the start time of the failure is uncertain because the project was rarely built outside of the centralized build infrastructure (where it worked fine). 10 cumulative hours of debugging across four developers was spent to figure this out.
In my experience, these kinds of "WTF" errors happen more often than the ones that make you go "wow, I am stupid". At least when you reach a skill level where the obvious problems don't show up so often.
But the point stands that this requires an uncommon kind of patience. Hooray, we solved it. Now we are finally able to modify the back-end behavior of this specific type of mutual fund order, which is what we wanted in the first place. Think the finance part of the task is more interesting than the banging your head against the wall debugging the tech stack part? Tough luck! Should have been born at the time when this happened by manually operating a terminal in the back office.
Yet another advantage to home working!