Yeah the doppler in this picture is all wrong unfortunately, the underlying equation used isn't right here (they mixed up spectral radiance and radiant flux). The rendering is also done without taking into account sRGB, and its run through a function that messes with the brightness - so the brightness is really incorrect. Plus all the colours are wrong (it uses an amhot colouring function, they aren't based on anything), and the extinction and emissivity isn't correct either, and the camera basis is also set up wrong so it also has the wrong perspective too. Other than that its all good

One side of the accretion disk is indeed brighter than the other – in the default view in the app, the bottom part is brighter. The effect appears quite clearly visible to me, although the exact contrast depends on the colorscale mapping. Here, I tried to find a colorscale that works well for both the disk and the jet, which naturally means the leading/trailing edge contrast can be less than in the linear mapping. Hope it explains the visual effect!

Kerr vs Schwarzschild (static vs rotating black holes) is a much smaller effect visually – that's why it is so hard for us to measure black hole spins (= how fast they are rotating) observationally, even with the Event Horizon Telescope.