Servo motor with a ultrasonic sensor

[groundFungus]

@superspeedyy

 duration_us = map(distance_cm, 0, 1023, 0, 255);
 Serial.print("A0 distance = "); Serial.println(duration_us);  // print the value of duration_us
  myServo.write(distance_cm);

Insert a print as shown to monitor the value of duration_us. Servos usually only go to 180°. Trying to run it beyond 180° can cause damage.

What is connected to A0? That is the only reading that you use, the rangefinder output is ignored.
You print the rangefinder output, but use A0.