I’m sure this could be put together with existing various features, but this could be made into something more straightforward and easy to understand. Perhaps as a condition that would be used in a choose action.
Example: An automation sends a notification on button press, then has a delay of 5 minutes.
First press: Trigger automation - Send a notification that says, “can you help me out?”
Second press: Automation is triggered and restart count is 1 - Send a notification: “I need your help!”
Third press: Automation is triggered and restart count is 2 - Send a notification as a critical alert: “SOS EMERGENCY!” Blink all lights, play a sound.