How/when did the trope of bad Soviet engineering develop in the West? Was this part of a delibrate propaganda campaign?

I don't know exactly when the trope "developed" in the West. But the Soviet Union attempted to industrialize quite rapidly in the 1920s, and it did so by bringing in American experts to help direct megaprojects like the Dniepier dam. Those American experts returned home and told many stories about how the Soviets were relatively "rough" in comparison to the Americans — they lacked precision industry, they lacked industrial experience. Their "engineering style" tended towards the easily-fixed and interchangable, as opposed to the bleeding-edge of optimization (the latter of which being the American engineering "style" esp. in the Cold War). This is not an unfair assessment — it is the difference, say, between the AK-47 (a relatively imprecise weapon that can be manufactured cheaply, repaired by just about anyone, and can put up with extremely poor working conditions) and the M-16 (a very precise and expensive weapon that, at least in its earlier versions, could not cope with adverse environments very well, was prone to jamming, etc.). There are many other examples of this.

As for when the trope became common; by the 1940s, US officials and industrialists spoke of the Soviet engineering capabilities in this way. I suspect earlier than that. I don't think it was part of a propaganda campaign that I have seen.