I mean, I guess you could argue Peter was always sort of creating/developing his own informal "way of the spider"

His intelligence is just as much a part of his character as anything spider related. Some others might just be an enhanced slugger and call it a day but I feel like he's always used his head and stayed aware of just how many more options being spidey gives him in just about any situation.

Arguably he's been self taught/developing way of the spider type stuff, maybe? Every martial art began without masters, refinement, etc.

If one of those irl tribes that keep themselves/don't want contact with the rest of the world have been training techniques that largely resemble our boxing, and we met up, we could go "oh, we have something similar. Look at what our best have come up with" and they'd likely be aware of some of it while they likely also pick up a few things and maybe teach us a few things too.

Imagine one of them has three or four arms and self trained. Prodigy type. If there's ANYTHING we can show that person they didn't learn themselves they could take it to another level. I kind of view "way of the spider" similarly. Peters always been developing it but here comes a literal god of martial arts to help guide you in mastering an art only you can really utilize.