Interestingly, there are LaTeX packages for coffee stains[1] and to simulate the variability of an actual typewriter[2]. I suppose both of these involve discrete objects (the coffee stain, individual characters) and photocopy/scan effects involve 'fuzzing' of the whole image, rather than any particular element, and TeX isn't really set up for the former.
Ironically, despite being hosted on tex.stackexchange.com, all of the answers use ImageMagick, Photoshop, or Windows 10/Adobe Acrobat.