I'm not sure it's really a thing in Pokemon... or, from a different perspective, all of it is. By nature Pokemon fanfiction tends to involve a lot more action sequences than other fics to the point where not being able to write a fight scene at all kind of limits you in the genera. Especially in the ever-present journey fic. Indeed to a certain extent the average journey fic is an action story since you have a main character who wants to be the best at a certain fighting technique who usually ends up having to battle off hordes of evil minions of a distant villain while effectively alone or with a small group of badass friends. So action.
On the flip side, if we count journey as something else entirely there just aren't many action Pokemon stories. Perhaps because every story has action elements it's kind of boring to just see lots of battles in a row with little to no plot. There are a dozen high quality options I could find on ff.net in an hour that have satisfactory action and plot/character development. So I think that really hurts straight action as a genera.
Of course, sometimes "THE VILLAINS TAKE OVER THE WORLD/UNITE!!!" fics happen and those tend to be straight action. But they are comparatively rare in the fandom and usually get abandoned pretty early on because they make less sense the more you think about them.
Vaira
I try to return reviews, but it might take me a while in bad weeks.