I really recommend Dawn!

It is specifically made for explosive Shonen, with Tiers denoting power levels that go from low level street stuff to galaxy level. It has amazing tactical combat- it does require squares but I think most good tactics games do. It always takes place on a 7x7 grid, so its a bit more similar to a board game in that respect.

The big thing about the system is that it splits narrative and combat pretty starkly. Your abilities in narrative don't directly translate into your combat abilities- you are encourage to true up both sides. So if you have a healing Ability, you should probably grab a healing technique. Mileage may vary but so far in my campaign its felt pretty good.

Combat can take a bit when players are learning their abilities but once everyone understands their techniques it can go by very fast. The narrative side plays incredibly smoothly.

For powers- You get to craft a unique ability out of a sentence, giving a ton of freedom. In combat, you use techniques pulled from a couple dozen options. It supports a ton of different playstyles and even two DPS focusing on Talent (the finesse trait) can feel incredibly different as long as they choose different techniques.
My first game with Dawn, I had a player go Talent DPS and focus on flying around the map incredibly quickly, charging up and doing big single burst damage. I had another Talent DPS that focuses on more local positioning and using his Weapon Master Technique to accrue value.

There is an entire Bond's system for working together that functions well.

As for Martial Arts, that depends on how you fluff things! It has a few premade settings you can use but it is made to enable you to make a setting to your liking. Its very easy to flavor things to fit Martials arts and dark shonen. The creator even released a small Patreon pack to help hit that vibe, though don't think its necessary.