For the first time ever, the Sony anti-dust feature worked for me. While I had to do it twice (the first time the chunky only moved around), the second time got rid of it.
It appears to be ultrasonic in the Sony A1, quite a difference from the worthless vibrate/rumble behavior of previous cameras.
In addition to this nice upgrade, the A1 offers the option to close the shutter when the camera is powered off. So if you turn the camera off prior to changing a lens, the shutter prevents dust from getting directly onto the sensor, although it can still get onto the shutter and the area in front of it.
Together, this might be the best Sony mirrorless camera yet for avoiding dust. But maybe other newer models like the Sony A7S III also have it?