Mayor Bill de Blasio on Thursday signed into a law a package of bills, one of which will prevent felons convicted of betraying the public trust from running for city office again. Such a bill would disqualify people like former state Senator and City Councilmember Hiram Monserrate — a twice-disgraced ex-lawmaker from Queens still seeking public office — from running for mayor, public advocate, comptroller, borough president, or city council.  While he comes to mind for many, the bill’s prime sponsor said his legislation is about more…