[magicalhippo]

Here's[1] a more concrete source, which summarizes dithering in analog to digital converters as follows:

With no dither, each analog input voltage is assigned one and only one code. Thus, there is no difference in the output for voltages located on the same ‘‘step’’ of the ADC’s ‘‘staircase’’ transfer curve. With dither, each analog input voltage is assigned a probability distribution for being in one of several digital codes. Now, different voltages with-in the same ‘‘step’’ of the original ADC transfer function are assigned different probability distributions. Thus, one can see how the resolution of an ADC can be improved to below an LSB.

In actual film, I presume the random inconsistencies of the individual silver halide grains is the noise source, and when watching such a film, I presume the eyes are doing the averaging through persistence of vision[2].

In either case, a key point is that you can't bring back any details by adding noise after the fact.

[1]: https://www.ti.com/lit/an/snoa232/snoa232.pdf section 3.0 - Dither

[2]: https://en.wikipedia.org/wiki/Persistence_of_vision

[adgjlsfhk1]

One thing worth noting is that this extra detail from dithering can be recovered when denoising by storing the image to higher precision. This is a lot of the reason 10 bit AV1 is so popular. It turns out that by adding extra bits of image, you end up with an image that is easier to compress accurately since the encoder has lower error from quantization.