@Django is correct - face detect AF can and will switch faces if there is more than one person in the frame. I haven't shot at high ISOs yet, maybe I'll do some low light shooting this weekend.
On another note, one of Sony's disadvantages (too small for my hands) also turns out to be one of its strong suits. I never had much luck balancing my GH5 with many of my favorite lenses on the original Zhiyun Crane, but for some reason, it's a breeze with the a7 III - the 85mm f/1.8 is a piece of cake, and even the fairly massive 35mm f/1.4 is doable without great effort. Which is important, because none of my lenses are stabilized and I shake quite a bit. And although the camera is small, even the 35mm lens doesn't protrude beyond the camera body. Lastly, I haven't used the a7 III on the gimbal long enough to be 100% certain of this, but it seems I can tighten the baseplate screw in the bottom of the a7 III enough to prevent the camera from twisting with heavier lenses, whereas with the GH5, whenever I used a slightly bulky lens, the camera always managed to work itself loose.