This reminds me of playing Lands of Lore, installed from a pile of floppies, back when. After installation, it went on to do something like "building color maps" or something like that. I have no details memory of exactly what it said or did, but on the hardware at the time it took FOREVER. Dozens of minutes. It was a one-time process though.

Audio shaders do, in fact, exist.

https://github.com/audiojs/audio-shader

why not just call these effects...

Shader is the term that's been established for these pieces of code that run on the GPU. (And yes, they're actual code that compiles down to machine instructions that run on the GPU.)

I think they may have originated with actually shading things, in a less technical use of the term; even today, the fragment shader's usual job is to output a color that the user would then see on the screen.

HZD does 1, and in fact can start without it. It just makes the loading times in game longer because it compiles shaders on the fly for the areas youre entering, and of course, being a CPU/GPU function, the loading times are not helped by an SAD when this occurs.

EDIT TO ADD
RPCS3 seems to compile sharers the first time you run a game, then save it for future use on subsequent starts of that game, unless you change certain settings. Is this unreasonable to expect ports to do the same, or is it much the same thing?

What about this shader pre-caching, downloading pre-compiled GPU shaders? See image in https://www.gog.com/forum/general/2_things_shader_heavy_pc_games_should_do/post13

as i see these are just simple scripts to make some gpu effects, are there so many gpu types devs can't precompile these? and how much space do these take?