Does GStreamer have any film grain effect element?
Something like Super 8 or 35mm film grain overlay?
There’s the agingtv effect element, but probably not quite what you’re looking for.
I was trying that, but it does not have the film grain effect. 
I was looking for something like this: GitHub - aabalke33/film-grain-effect: Overlays film grain to a still image or frames of a video.
There’s probably some film grain synthesis code in AV1 decoders?
Yes, that is exactly what I wanted to try out. So I wanted to insert some film grain in test content and check how AV1 would encode it. 
Turns out that the frei0r-filter-lib-frei0r-1-rgbnoise element does a pretty good job at adding some cool noise.