Is there a feature in DJI Mini 3 Pro to track a flying object but from a stationary position (hovering)? For example, to pan and tilt the camera to follow an object? Thank you.

you mean as if mounted on a tripod?   skydio has it, not sure i've seen it on the dji.

SpotLight mode allows you to track a pre-selected object. Manual v1.4, page 20-22

Hi, AndrewRH. Thank you for reaching out. You may try using the Spotlight 2.0 feature like Drone.Hunter mentioned above. It will allow you to control the aircraft manually while the camera remains locked on the subject. The mode supports the capturing of both stationary and moving subjects such as vehicles and people. Move the roll stick to circle the subject, pitch stick to alter the distance from the subject, throttle stick to change the altitude, and yaw stick to adjust the frame. In Spotlight mode, when the vision systems are working normally, the aircraft will hover if an obstacle is
detected, regardless of whether the obstacle avoidance behavior is set to Bypass or Brake in DJI Fly. Note that obstacle avoidance is disabled in Sport mode. We hope this helps. Thank you for your continued support.