Welcome to the forums @dmitrykolesnikovich!
I do not know where the compiler code is, but Godot uses its own shader language loosely based on GLSL. This shader language is compiled to GLSL in Godot 3.
From my limited understanding, in Godot 4 it will be compiled to GLSL for OpenGL 2, SPIR-V to Vulkan, and SPIR-V to Metal for iOS and MacOS (via MoltanVK). The tweets by Reduz and the replies to them have a bit more information:
https://twitter.com/reduzio/status/1252052089762693120
There is also a bit about the Vulkan shader stuff in the Vulkan Progress Report 2 but it does not really go into any detail. Future Vulkan progress reports may also have information about it.
If you are curious about how Godot handles shaders across so many APIs, I would suggest going to the devel level on the IRC or the engine development channel on the Discord (I think there is, I have not used Discord TBH). Either way, the core Godot developers on either community that can probably answer roughly where the code is for compiling shaders on multiple targets and where to look.
