I don't see how it's so traumatic for the engineers involved, unless the company culture in Fastly is really awful and there are punitive repercussions, or attempts to pin responsbility on individuals rather than systems, which I doubt.
Many here have been responsible for web service outages albeit on much smaller scales, and in my experience it feels awful while it's happening but you quickly forget about it because so does everyone else.
I guess it very much depends on your personality. I screwed up a a not very important project for a client 4 years ago while working at a different company, and I still feel bad when I think about it, despite the fact that my company had my back through the entire process and literally everybody involved has moved on and probably forgotten about it.
Many here have been responsible for web service outages albeit on much smaller scales, and in my experience it feels awful while it's happening but you quickly forget about it because so does everyone else.