are we talking about compiled game shaders or project shaders? From what i found, project shaders are cached in /my-project/.godot/shader_cache
Not sure where the compiled game shaders live. I am interested in this too 
EDIT:
I also found (on binbows) in the appdata folder:
C:\Users\username\AppData\Roaming\Godot
Also under app_userdata\my_project
Not sure if these are the compiled game dirs or just project garbage data..
MikeCL Does anyone know how to easily find and remove the compiled shader cache?
I'm guessing it may not be engine or game related, and you should probably look elsewhere. Probably in the system.
But I could be wrong.
Tomcat what about linux or bigmac and amd? I tried to look for my godot shader folders from compiled games i had run in the past. and i could not point directly to it.. Nvidia shaders are encoded and you have no way to tell wich are for what game.. I dont know where amd shaders live on linux..
Isnt shaders recompile each time you change something? On steam on linux every day a game updates, it recompiles shaders before it launches a game.. not sure how it happens on windows..
kuligs2 what about linux or bigmac and amd?
…
On steam
That is, it has to be sought for each particular system and case.
The docs don't have a lot of info about it. The only thing I found was:
https://docs.godotengine.org/en/stable/tutorials/performance/pipeline_compilations.html
Drivers usually keep a cache of pipelines stored somewhere in the system to avoid repeating the process every time a game is run. This cache is usually deleted when the driver is updated.
"Somewhere" 
For Nvdia it seems to be:
%LocalAppData%\NVIDIA\DXCache for DirectX
%LocalAppData%\NVIDIA\GLCache for OpenGL and Vulkan
I'm not sure if you can actually delete certain cached shaders from what I've read. But I'd like to know that too. It would be useful for testing your game.
EDIT:
Under C:\Users\Username\AppData\Roaming\Godot\app_userdata\Projectname\vulkan I found this:
Interesting, I thought this was more controlled by the engine/the game.
I wonder what a good way to control this would be.
I'm building a simple system for my game that will compile and cache the shaders when you run the game the first time. And skip this process if the shaders have already been cached.
And I also want the player to be able to specify if they want to re-compile the shaders again. I took inspiration for how Delta force handles this (probably a lot of games that does it the same way, just noticed it in that game and thought it's a good workaround).
But for this to work I need some simple control.
trizZzle Under C:\Users\Username\AppData\Roaming\Godot\app_userdata\Projectname\vulkan I found this:
I'm assuming this is for the editor/engine?
Interesting that it's not that easy to find information on this as it's a pretty common issue on PC specifically (stutters etc)
MikeCL
I think this is one of the main features of Godot 4.4 that it precompiles shaders in a way that you shouldn't get stutters in the game anymore.
About the shader_cache:
As I had some problems in Godot 4.4 that my game wouldn't run from the Editor because of shader_chache problems I can say that this place was the active one:
C:\Users\Username\AppData\Roaming\Godot\app_userdata\Projectname\
not the .godot folder in the project itself.
(Godot 4.4.1 solved my issues)
When I delete this Folder and run the exported Game then this is also the place it gets created.
Before 4.4 stutters from shaders were a huge problem eg. for the Dev of this game and he talks about his solutions here:
musikai Thanks for sharing!
Smart that he created a python script for it. I'm thinking that a GDScript could be created for this as well.
Ah.. yes.. I'm still on 4.2.2. But didn't only 4.4.1 minimize the issue and not completely remove it? Maybe I remember it wrong, but I think I read somewhere a long time ago when this was talked about that there might still be stutter, but much less?
Maybe this article will clarify something:
musikai this does not solve the compiled game shader cache.. the compiled game shaders live somewhere else rather than app_userdata/project_name
Tomcat how to clear shader cache for dummy's
That is, it has to be sought for each particular system and case.
I wonder where are the non steam game shaders cached?
On linux i found a folder under .cache/AMD rather something.. but as per usual files are encrypted and not human readable so you dont know which ones are for your game or not.
MikeCL I'm building a simple system for my game that will compile and cache the shaders when you run the game the first time. And skip this process if the shaders have already been cached.
Isnt game itself precompiles them when you launch it?
MikeCL And I also want the player to be able to specify if they want to re-compile the shaders again. I took inspiration for how Delta force handles this (probably a lot of games that does it the same way, just noticed it in that game and thought it's a good workaround).
i dont know how they do it, but from what i saw with AMD on linux. Every time a game updates, steam recompiles shaders before game launches.. Im not sure if the engine requests that to steam API or how ..
It would be nice to know tho
kuligs2 Isnt game itself precompiles them when you launch it?
The shaders compiles the first time they are rendered as I understand it (feel free to correct me if this is wrong). That's the reason there's stutters when things enter the camera view for the first time.
kuligs2 Every time a game updates, steam recompiles shaders before game launches
I would love to hear from someone that has launched a Steam game on this. If this also applies to Godot games? Wouldn't Godot need an Api to trigger shader compilation for this?
I couldn't find anything that explains how this works in depth. Though it was turned on all the time it still says 0 MB.
Why does it cost bandwith if Steam collects the shaders from my system?
EDIT: Does Steam look which shaders I need and instead of letting the game compile them it looks and downloads already compiled ones?
This is really an interesting and confusing topic. 
what steam does is steams problem, game should function whithout third party apps.. IMO.. I would like to know how to precompile shaders too, cuz on heavy 3d games it really feels bad experience when they keep compiling during gameplay.. unplayable..
trizZzle I'm a little confused. What would be the purpose of this? I mean, wouldn't the shaders need to be compiled and cached anyway? Or is it that with this that the Godot game (a Steam-installed one) would look at the Godot cached folders and copy over the already cached shaders from your system? But that would only work on your machine as a dev since you will be the only one having the game before release. If this is the case, I don't see how this helps the customer who bought your game.
And why would Steam have its own cache (if it's for shaders)?
trizZzle This is really an interesting and confusing topic.
Indeed
MikeCL I'm a little confused. What would be the purpose of this? I mean, wouldn't the shaders need to be compiled and cached anyway? Or is it that with this that the Godot game (a Steam-installed one) would look at the Godot cached folders and copy over the already cached shaders from your system? But that would only work on your machine as a dev since you will be the only one having the game before release. If this is the case, I don't see how this helps the customer who bought your game.
And why would Steam have its own cache (if it's for shaders)?
I absolutely have no clue, so far I can't make any sense of that. But I will continue looking for answers. It's something I'm curious about as well.
