During the part of the game where the player reaches one of the beginning mobility gel tests, there's a bunch of "stadium lights" that all turn on at the same time, then the player gets a quick temporary overlay of pure whiteness. What is needed in the map editor to create GUI overlay effects like that?

env_fade with the fade color white?
I'd go into more detail but not sure if this is correct.

That is correct. I used these settings:

env_fade.png

Send it a "Fade" signal to trigger the screen flash.
You may want to experiment with different time values and colours, to get it to look right in your map.

Modulate is good for effects like that.

I see. Is there something that can be used in hammer to create the GUI overlays such as when you get covered in gel? Or is that something that's hardcoded?

Edit: Nevermind.

It's hardcoded, but you can use an info_particle_system with the boomer vomit effect to get a form of it. IDK what color it is by default, but you can use the Particle Editor to make different ones.