Inject `compiler_builtins` during postprocessing and ensure it is made private
Follow up of https://github.com/rust-lang/rust/pull/135278
Do the following:
* Inject `compiler_builtins` during postprocessing, rather than injecting `extern crate compiler_builtins as _` into the AST
* Do not make dependencies of `std` private by default (this was added in #135278)
* Make sure sysroot crates correctly mark their dependencies private/public
* Ensure that marking a dependency private makes its dependents private by default as well, unless otherwise specified
* Do the `compiler_builtins` update that has been blocked on this
There is more detail in the commit messages. This includes the changes I was working on in https://github.com/rust-lang/rust/pull/136226.
try-job: test-various
try-job: x86_64-msvc-1
try-job: x86_64-msvc-2
try-job: i686-mingw-1
try-job: i686-mingw-2
1610bfb6af