I tried googling and I got a lot of hits for what reader mode does and how to enable it, but nobody can explain what the browser is actually doing.
Do sites have pared-down versions of their pages specifically for reader mode? Or does the browser just scan for particular HTML tags?


I believe this is due to ADA Title III requirements for publicly accessible businesses:
https://www.ada.gov/resources/web-guidance/
Screen readers and braille displays can’t do anything with all the fancy JavaScript and other nonsense that frames and formats the content for delivery, including the user-identifying-and-blocking stuff. The website is legally required to make the content accessible in a way that assistive technologies can use, and usually the simplest way to do that is to just deliver plain text. I think “reader mode” is leveraging this functionality to get the content in a simple form without the cruft, basically just telling the website that the user needs the ADA compliant version.