Im not seeing much about it online. is there a real point to doing all of the story/is chapter 4 unlocked? i have an option to "press Enter" to unlock chapter 4 but nothing is happening. Can anyone help?

You get partner cards for certain characters that you would otherwise not get.

@coldreactive is chapter 4 available to NA yet?

No chapter 4 yet. You also get a fair amount of Star Gems for doing the story.

Yes, each time you would have received a matter board (Or, "Matrix Divergence" it's called here.) You get 10 SG instead.

Make sure to do up to a certain point with the current event going on giving rewards