The LSB of samples from a gaussian distribution is uniformly distributed: 50/50 chance of 0/1

(Assuming you have enough bits per sample which image sensors provide IRL)

Only in theory. In practice, they're correlated with the other bits and adjacent pixels.

How correlated? I spent 2 minutes trying and failing to get chatGPT to generate code that downloads an image dataset and runs diehard on the LSBs. I'd expect the LSBs to pass the randomness test.