Sweet understanding, or manually implementing backpropagation

Recently I've been watching lots of fun-purportedly-educational videos which have strikingly beautiful graphics but leave me unsure if I've actually absorbed anything at all.

And then a few days ago I realized that I've never manually implemented backpropagation (despite being a ML engineer (urg) (?)).

I'm reminded of the early days of algorithms classes. I was obviously gaining some level of understanding. But what level? I know how to implement quicksort. But I also know that implementing it is different from being able to have invented it. And, paradoxically, the more I studied, the more acutely I began to sense that I could not have made the discovery.

I suspect that I crippled myself by stopping the problems as soon as I'd gotten the answers. In literary criticism it's normal to read an essay, then read a refutation of the essay, and then read a refutation of the refutation, and so on. I don't know if it's common to work proofs in math as hard, to figure out multiple ways to solve a problem even when one path is already apparent. I certainly didn't.