Hold up. That entire image is 8-bit. It’s a JPEG image. JPEG can’t encode more than 8 bits per channel. Nor can most displays, including mine, display more than 8 bits per channel. And yet the left half of your image exhibits far worse banding than the right half.
The left half looks more like 5 bits per channel rather than 8. You’d see that kind of banding in gradients back in the days of Windows 3.1, when 16-bit color was common. (16-bit color uses 5 bits each for red and blue, and 6 bits for green.)