Preserve filesystem permission path conventions (#39084)

## Why

Filesystem permission paths can use a convention that differs from the host
running Codex. Converting them immediately to native absolute paths can change
the meaning of ambiguous paths such as `/C:/secret` or Windows UNC paths.

## What changed

- Store literal filesystem permission paths as `PathUri` values through the
  runtime policy and execution protocol.
- Keep legacy string-based serialization at explicit protocol boundaries and
  reject conversions that cannot be represented losslessly.
- Encode native paths as opaque URIs when a normal file URI would imply the
  wrong path convention.

## Testing

Added coverage for cross-platform and ambiguous path round trips, UNC path
variants, permission-profile serialization, and deny-policy enforcement.

GitOrigin-RevId: 5247713796d1f2bb4e02f94eb9fc82d4698060f0

codex-rs/utils/path-uri/src/api_path_string_tests.rs

@@ -82,8 +82,8 @@ const RENDER_CASES: &[RenderCase] = &[
     ),
     RenderCase::round_trips("file:///etc", PathConvention::Posix, "/etc"),
     RenderCase::round_trips("file:///tmp/", PathConvention::Posix, "/tmp/"),
-    RenderCase::round_trips("file:///C:/Project", PathConvention::Posix, "/C:/Project"),
-    RenderCase::round_trips("file:///C:", PathConvention::Posix, "/C:"),
+    RenderCase::renders_lossily("file:///C:/Project", PathConvention::Posix, "/C:/Project"),
+    RenderCase::renders_lossily("file:///C:", PathConvention::Posix, "/C:"),
     RenderCase::round_trips("file:///tmp/%E2%98%83", PathConvention::Posix, "/tmp/☃"),
     RenderCase::round_trips("file:///tmp/a%5Cb", PathConvention::Posix, "/tmp/a\\b"),
     RenderCase::round_trips(
@@ -466,6 +466,19 @@ fn converts_absolute_api_paths_using_the_inferred_convention() {
     }
 }
 
+#[test]
+fn ambiguous_absolute_api_paths_preserve_their_inferred_convention() {
+    for (raw_path, convention) in [
+        ("/C:/secret", PathConvention::Posix),
+        (r"\\localhost\share", PathConvention::Windows),
+    ] {
+        let path = LegacyAppPathString::from_string(raw_path);
+        let uri = PathUri::try_from(path.clone()).expect("absolute API path should convert");
+        assert_eq!(uri.infer_path_convention(), Some(convention));
+        assert_eq!(LegacyAppPathString::from(uri), path);
+    }
+}
+
 #[test]
 fn converts_native_api_path_to_inferred_absolute_path() {
     #[cfg(windows)]