SPRINGFIELD — Illinois lawmakers passed 566 bills through both chambers of the General Assembly in the recently concluded legislative session – all but one of them in May.It sets the table for an approximate three-month bill-signing season for Gov. J.B. Pritzker. That’s because the state’s constitution gives legislative leaders 30 days from a bill’s passage to send it to the governor, who then has 60 days to sign or veto it.If the governor takes no action in that time frame, the bill would …