This year’s final New York state budget includes a pot of money meant for “stabilizing the correctional system,” an effort to address the ongoing fallout from a three-week corrections officer strike last year.The amount is hefty: $535 million on top of the prison agency’s roughly $4 billion annual budget. While much of the money will likely go to the National Guard, whose troops have been covering unstaffed prison posts for over a year, the budg…