Way back in 2014 Canon introduced a feature with the 7D Mark II that they called flicker reduction. Basically, the camera uses the light meter to detect the timing of flickering lights and then times the shutter release so that the middle of the exposure coincides with the peak of flickering lights. Remember, with focal plane shutters the time difference between the movement of the first and second shutter curtains is what establishes exposure time. The shutter curtains always move across the frame at the same speed. The total transit time of each shutter curtain is always the same for a given camera, regardless of the selected "shutter speed". Thus, for any given camera, opening the first curtain x/2 milliseconds before the light peaks, where x is the shutter curtain transit time in milliseconds, insures that the peak of the light occurs at the halfway point in the total transit time of the first curtain. With most AC powered lights this results in a fairly evenly exposed frame because the cycle of the light's flicker is sinusoidal, which means the intensity changes less per time unit at the top and bottom of the cycle than it changes at the mid-point in the cycle.

This was primarily intended to help sports shooters working under flickering artificial lighting use shorter exposure times without suffering the effects of the flickering lights when the exposure occurs at the mid-point or low-point of the flickering light cycle. It has proved to work very well. Personally, I never intended to buy another APS-C camera until the introduction of the 7D Mark II with the feature. When shooting field sports at night with a 70-200mm f/2.8 lens I went from getting about two or three out of every ten frames with good, balanced light and color from one side of the frame to the other when shooting at around 1/800-1/1000 seconds with the 7D to getting between nine and ten good frames (in terms of brightness and color, LOL) out of a ten shot burst when using the 7D Mark II with the flicker reduction turned on.

Canon has included the feature on most of their higher than entry level cameras since that time, and even include it on some entry level DSLRs and all mirrorless cameras as of 2020. It has been very well received.

The Sony α9, introduced in 2017, uses a similar scheme to time the shutter release, whether mechanical or electronic, with the detected peak of the light in the scene. Just as the transit time of a shutter curtain remains constant in most modern cameras with focal plane shutters, the scanning time of a sensor using electronic shutter also remains constant over various exposure times. It's the difference between "on" and "off" for each line that determines the exposure time. That's probably why you're not seeing it near as much or at all with the α9 as with the α7 III. Since the α7 III was not intended to primarily be a "sports" type camera like the α9, and since it has a much slower readout sensor, it probably does not include the feature.