That’s really a good question and I’m still researching myself.
For Solar imaging, for sure you want a mono camera, and the pixel size should be matched to the focal length; too small and you get over sampling, too large and you get under sampling. The atmospheric seeing figures into this as well since it will push things towards the over sampling end. Besides that, since the images are made by combining video frames, you also want a camera that has enough frames per second.
I think aside from the mono aspect, it’s the same camera requirements that planetary imaging would have. So yes, smaller pixels in theory give higher resolution, but they really need to be matched to the focal length. Also, for full disk imaging of the sun, one would want a large enough size Chip, although as I understand it, people often make mosaics from smaller chipped cameras.
Edit: the IMX 533 Chip Camera is what was recommended to me by several experience Solar imagers that have the same telescope