https://graphics.stanford.edu/courses/cs248-04/ho6/
Of course sharpness is a function of resolution. I'm not sure it makes sense to talk about capacity, because typically the resolution of the image is non-negotiable. The number of bits needed to encode it is variable and depends on compression technique used.
So in general, Shannon-style channel thinking operates on a different layer from the sampling and reconstruction processes we are discussing here. It's more relevant to how discrete pixel values are coded, or more elaborate compression mechanisms which exploit coherence in the image.
To perform this tradeoff and capture e.g 1-bit images with super-high resolution you'd need the sensor to do error diffusion a la sigma-delta modulation, and AFAIK image sensors cannot currently do this.
Typical root raised cosine filters are used, as it is a matched filter for itself, and minimizes ISI depending on the bandwidth chosen.
I suppose Shannon’s capacity theorem can be applied to images, trading off bandwidth for SNR. If resolution is bandwidth, and brightness the SNR, what would capacity be in a photo? The sharpness? That would imply sharper photos would be better off with higher pixel sensors than with dynamic range. You can always decimate to increase SNR.
In electronics, it’s easier to make faster converters than increase dynamic range, so oversample and decimate. Same probably with image sensors.