It doesn't really have anything to do with that. Trump just wants NY to stop the lawsuits against him. All the rest of his reasons are just bullshine.
In other words, its just ANOTHER abuse of power quid pro quo. But since the Senate acquitted him in the Ukraine deal, he's free to abuse the power of the Presidency as often as he likes.
Remember the Checks and Balances theory you learned about in 5th grade civices? The Senate just wiped that slate clean.