Also, in the books (which I should admit I’ve not read), what exactly were the BG expecting would happen after creating their Quisatz Hadderach? I can’t conceive of how they would hope to retain control or, perhaps rather, how their usual manipulation strategies wouldn’t have blown up in their faces. Would the person they were looking for be so vulnerable in that way? Would they not still have the capacity to retaliate?
For a while, Paul was set on preventing the jihad; he could see enough of the future to know that it dominated many of his possible futures, but still had hope that he could navigate a path that avoided it.
Eventually, however, the cruelty of those in power - and apparently becoming a target of the Emperor himself - caused Paul to give up on that goal, and resign himself to his fate of being the rallying point of the jihad. Whether or not his foresight was dominated by the visions of the wars to come was because of this decision is an exercise for the reader. Probably, though; Paul failed to take into account how the future would shape his psyche. Originally he seemed to think that the jihad would happen against his will.
As for the BG, they expected the Kwisatz Haderach to be one of their own, raised by them and shaped to cement their power. Again, it was circumstance that turned Paul against them. Although he had been trained by Jessica, and tested by the Reverend Mother, he was only barely on the verge of being able to fulfill the criteria they needed. Their expected KH was supposed to happen later, in a more controlled environment. Instead, he came into his power unexpectedly on Arrakis, and he suffered so much due to the machinations of the great houses and, by extension, the BG themselves that there was no controlling him.