Use public-dependencies in all sysroot crates

In [1], most dependencies of `std` and other sysroot crates were marked
private, but this did not happen for `alloc` and `test`. Update these
here, marking public standard library crates as the only non-private
dependencies.

[1]: #111076

compiler/rustc_codegen_cranelift/patches/0029-stdlib-Disable-f16-and-f128-in-compiler-builtins.patch

@@ -15,7 +15,7 @@ index 7165c3e48af..968552ad435 100644
  edition = "2021"
 
  [dependencies]
- core = { path = "../core" }
+ core = { path = "../core", public = true }
 -compiler_builtins = { version = "=0.1.146", features = ['rustc-dep-of-std'] }
 +compiler_builtins = { version = "=0.1.146", features = ['rustc-dep-of-std', 'no-f16-f128'] }
 

library/alloc/Cargo.toml

@@ -1,3 +1,5 @@
+cargo-features = ["public-dependency"]
+
 [package]
 name = "alloc"
 version = "0.0.0"
@@ -9,7 +11,7 @@ autobenches = false
 edition = "2021"
 
 [dependencies]
-core = { path = "../core" }
+core = { path = "../core", public = true }
 compiler_builtins = { version = "=0.1.146", features = ['rustc-dep-of-std'] }
 
 [dev-dependencies]

library/sysroot/Cargo.toml

@@ -1,14 +1,16 @@
+cargo-features = ["public-dependency"]
+
 [package]
 name = "sysroot"
 version = "0.0.0"
 edition = "2021"
 
 # this is a dummy crate to ensure that all required crates appear in the sysroot
 [dependencies]
-proc_macro = { path = "../proc_macro" }
+proc_macro = { path = "../proc_macro", public = true }
 profiler_builtins = { path = "../profiler_builtins", optional = true }
-std = { path = "../std" }
-test = { path = "../test" }
+std = { path = "../std", public = true }
+test = { path = "../test", public = true }
 
 # Forward features to the `std` crate as necessary
 [features]

library/test/Cargo.toml

@@ -1,12 +1,14 @@
+cargo-features = ["public-dependency"]
+
 [package]
 name = "test"
 version = "0.0.0"
 edition = "2021"
 
 [dependencies]
 getopts = { version = "0.2.21", features = ['rustc-dep-of-std'] }
-std = { path = "../std" }
-core = { path = "../core" }
+std = { path = "../std", public = true }
+core = { path = "../core", public = true }
 
 [target.'cfg(not(all(windows, target_env = "msvc")))'.dependencies]
 libc = { version = "0.2.150", default-features = false }