What was the quote about Feynman? That he loved to cultivate anecdotes about himself or something similar? Makes a lot of his stories make a lot more sense, too.
i recall him explaining several shortcuts one can use to solve problems in seemingly impossible speeds by drawing on a breadth of experience from similar problems that you have memorized or are easy to compute and interpolating.
its still genius but not in the sense of actually being able to do huge calculations in ones head the way a computer would.
Often it's also simply just that people are not used to thinking about more efficient ways of solving a problem.
There's a (quite possibly apocryphal) story about Niels Henrik Abel in primary school, where his teacher supposedly wanted time to do some grading and assigned the students the busywork of adding up all numbers from 1 to 100. Abel supposedly quickly found the well known formula n(n+1)/2 and gave the teacher the answer within minutes, and the teacher supposedly believed he'd somehow "cheated" because he could not imagine any of them could figure it out.
I have no idea if the story is real (I grew up in Norway, so Abel was a popular subject for stories like this) - it was told to me in high school by a maths teacher after giving us the modified task of seeing if we could find any shortcuts to doing the sums, and seeing what we'd come up with. I found the formula quickly, but at that age that's nothing special, especially not when prompted to find an alternative solution.
But the overall idea the teacher was trying to get us to understand was how to pause and think about how to decompose a problem rather than just picking the most obvious alternative, and learning to be "lazy" in the sense of relentlessly looking for an easier way to do things is a large part of what got me into software development..
Feynman has no dearth of stories showing his genius, but one specific example is a video 3Blue1Brown did of how Feynman converted the velocity vectors of a revolving body in a gravitational well (I think it was that) into a perfect circle of vectors. It's one of those results that's deep and yet you can find it yourself too if you spend enough time with it.
I think the part that makes it genuine is that he was comically self aware of himself and his craziness. Even when he was pushing the boundaries just for the sake of it and to make a caricature / character out of himself, he did it in a way that made me think that he didn't really pretend to not be doing it for his ego.
It's like 4 levels of thinking somehow merged in his actions: 1) be normal and look at the crazy people, 2) be a crazy person, 3) be a crazy person and be aware of your craziness, 4) be a crazy person, be aware of it and let others know that you're aware of it. It feels like one of those thought spirals I go into if I have weed. It's right on the boundary of crazy but probably also (in his case) inside the realm of genius.