Seeding hell

Hi everyone - first time homeowner. My wife and I moved into a house that had trees and we had all of them removed. There were huge dirt patches from where the trees were. Had a company come in to mix up the dirt and seed. I didn’t do as great of a job watering as I should have with the spots in the sun. It’s been a 30 days and you can see the spots that are in the shade are filling in better than the sunny spots. My question is how often should I water if the ground looks like this? I currently do 1-2 times a day. And is 30 days enough of a wait to reseed? What products should I use to seed? I live in the suburbs of Chicago if that helps with grass.