Please just think about the logical implications of it being independent of area.
https://medium.datadriveninvestor.com/how-to-create-awesome-noise-that-is-actually-real-cf178c9f0ae0>The standard deviation for the number of interactions per pixel is called photon shot noise.I can't speak to your DR vs ISO graphs and all that, I don't know enough about that stuff, and given that the argument is about theory not implementation, and all I'm asking you to do is prove your definition of shot noise or SNR is correct, I don't see the need to look at graphs.
