Match core skill ordering in extension catalogs (#34746)

## Why

Core-compatible catalog rendering needs to preserve the core renderer's skill
priority, including when metadata budgets omit lower-priority entries.

## What changed

- Carry each host skill's `SkillScope` into its catalog entry.
- Under `CoreCompatible`, order visible skills by system, admin, repo, and user
  scope, then by name and prompt resource ID.
- Preserve insertion order under `ExtensionCompatible`.

## Testing

Add coverage for propagating host skill scope and for both rendering policies.

GitOrigin-RevId: 9594a177edb2166abf1b5719c51a46fcee000600

codex-rs/ext/skills/src/provider/host.rs

@@ -116,6 +116,7 @@ fn catalog_entry_from_skill(skill: &SkillMetadata, enabled: bool) -> SkillCatalo
     )
     .with_short_description(skill.short_description.clone())
     .with_display_path(display_path)
+    .with_prompt_scope(skill.scope)
     .with_dependencies(skill.dependencies.clone());
 
     if !enabled {
@@ -127,3 +128,7 @@ fn catalog_entry_from_skill(skill: &SkillMetadata, enabled: bool) -> SkillCatalo
 
     entry
 }
+
+#[cfg(test)]
+#[path = "host_tests.rs"]
+mod tests;

codex-rs/ext/skills/src/provider/host_tests.rs

@@ -0,0 +1,54 @@
+use std::sync::Arc;
+use std::time::SystemTime;
+use std::time::UNIX_EPOCH;
+
+use codex_core_skills::loader::SkillRoot;
+use codex_core_skills::loader::load_skills_from_roots;
+use codex_exec_server::LOCAL_FS;
+use codex_protocol::protocol::SkillScope;
+use codex_utils_absolute_path::AbsolutePathBuf;
+use pretty_assertions::assert_eq;
+use tokio::sync::Semaphore;
+
+use super::catalog_from_outcome;
+
+#[tokio::test]
+async fn host_catalog_entries_carry_their_prompt_scope() -> Result<(), Box<dyn std::error::Error>> {
+    let unique = SystemTime::now().duration_since(UNIX_EPOCH)?.as_nanos();
+    let root = std::env::temp_dir().join(format!(
+        "codex-skills-extension-host-provider-{}-{unique}",
+        std::process::id()
+    ));
+    let skill_path = root.join("demo").join("SKILL.md");
+    std::fs::create_dir_all(
+        skill_path
+            .parent()
+            .ok_or("skill path should have a parent")?,
+    )?;
+    std::fs::write(
+        &skill_path,
+        "---\nname: demo\ndescription: Demo skill.\n---\n# Demo\n",
+    )?;
+    let root = AbsolutePathBuf::try_from(std::fs::canonicalize(root)?)?;
+    let outcome = load_skills_from_roots(
+        [SkillRoot {
+            path: root.clone(),
+            scope: SkillScope::User,
+            file_system: Arc::clone(&LOCAL_FS),
+            plugin_id: None,
+            plugin_namespace: None,
+            plugin_root: None,
+        }],
+        /*plugin_skill_snapshots*/ None,
+        Arc::new(Semaphore::new(1)),
+    )
+    .await;
+
+    let catalog = catalog_from_outcome(&outcome);
+
+    assert_eq!(catalog.entries.len(), 1);
+    assert_eq!(catalog.entries[0].prompt_scope(), Some(SkillScope::User));
+
+    std::fs::remove_dir_all(root.as_path())?;
+    Ok(())
+}