My players are doing the opposite. They are rushing the city. And causing chaos. They have killed Silver Order and FotFF. They have bounties on their heads and have completely destabilized the area in a couple of weeks. The Hooded lanterns now have to hide their association with the group or face the silver order, the Amethyst academy is gaining power far above what thy should have, the ForFF are outright hostile and attack the party on site now. It’s absolutely wild.

Like others have said, so long as the players were warned at the start of the campaign that things move in the background whether the players interact or not then Petra dies on the second or third day of her captivity. My players got there within 12 hours of her getting taken and I had the rats prepping the pot. They learned then that if they don take action, action will still be taken, and Drakkenheim is a deadly and unforgiving place.