Most companies don't have them at all. Not by that name or anything like it, and if they have anyone kinda doing a similar-ish job you'd probably find their role and practices dissimilar enough that you'd not call them that, either.
It's not.
I probably stopped trying to understand what it meant at the 3rd-4th paragraph. I feel I wasn't worth an explanation...
Did you Google it? It's the first thing that comes up.
Google customizes results per the logged in user, so "site reliability engineer" wouldn't necessarily be the first result for different people. Random list: https://www.abbreviations.com/SRE
google made the term popular. there is a book on it that kinda expands on what it entails.
It also stands for Software Reverse Engineering. An example is Ghidra [1]