If I fly forward at full speed (57kmh) in sport mode, the remaining time drops significantly. What about security? Does the drone reduce its speed or does it issue a warning message if you push the battery too hard?

Yes,  if you need more power then the battery can achieve it will throttle you back,  especially if fly into wind.  Sometimes it will show a battery overload warning and others not.

Hi there. The maximum flight time (34 minutes) claimed on the DJI official website is measured when the aircraft is flying at 21.6 kph in windless conditions (25°C) from taking off with a full battery level to the time when the aircraft triggers a low battery warning and automatically lands on the ground. However, during actual flight, due to environmental limitations (temperature, wind power, and air pressure), aircraft speed, and other factors, the maximum flight time may be decreased to different levels. Have a nice day.