The A/C compressor on the model 3 is a variable speed one, like most every other EV, but unlike ICE. This means if you leave the car in AUTO mode, and the cabin is hot, the compressor is going to ramp up to full speed to try and cool down the cabin. This is why it fades away as the car cools down, or after it runs for a bit of time. This is very much normal behavior. It's kinda loud and buzzy when running full speed, and the fan noise can be considerable as well depending on load and outdoor temperature. As the load or cabin temp decreases, the compressor speed will slow down and as a result it will get quieter.
Out of the handful of Model 3's ive heard running the A/C, they always made the same loud buzzing sound. Its expected and normal behavior. The steering wheel and even interior vibrates a little bit when the compressor is running flat out. If this bothers you, dropping the fan speed will effectively limit the compressor speed. The entire system is variable speed, and the fan outside will only run as much as required. Dropping the fan speed inside will limit how much heat the system can remove, and as a result should drop the fan/compressor speed outside. I think it would be nice if they had a 'quiet auto' mode that limited the fan/compressor speed a bit so it wasn't so loud at times.
