Does Initial D count?

non-action battle-shounen

The first thing that comes to mind when you say that is Yakitate Japan. Shokugeki comes to mind next as a newer take on the idea of cooking competitions. Let me know if I’m misunderstanding the wording though.

Akagi. Can I also count Saki as a battle shoujo?

Yakitate Japan is my favorite, but since it was already mentioned I guess I’ll say Akane Banashi. Ending isn’t written yet, so fingers crossed that it’ll be good!

Food Wars, pun intended

If by non-action, you mean anything that isn’t fighting, I like how Blue Lock made football a battle shounen.

Hikaru no Go. Shounen, yes. Competition, yes. Action? Even less than a cooking anime.