Look at Vatican city today. It is a country within a country. Does the Vatican execute anyone? No
Re: the time period you are speaking of
It was decided that the state isn’t to charge someone with heresy because that’s not their expertise. The Church is the vehicle for that decision.
The Church will investigate and if warranted, declare someone a heretic. The guilty person will always have a chance to recant. But If they don’t, the state also had an interest in that person. That’s why they were turned over to the state. The state then tried them for heresy. A crime in that time in history, heresy was equal to treason. It caused division and many times serious division within the state. The Church doesn’t/didn’t execute anyone. The state OTOH prosecuted someone for heresy, and if the state deemed it necessary, the state executes someone as an enemy of the state. That’s the order the law took in those days.
Today, pope Francis says, capital punishment isn’t necessary. Criminals can spend their life behind bars. Can he force a state or country from executing criminals? No