Move the host skills service into the skills extension (#36921)

## What changed

- Move host skill discovery, snapshot caching, and configuration handling from
  `codex-core-skills` to `codex-skills-extension`.
- Rename `SkillsService` and `SkillsLoadInput` to `HostSkillsService` and
  `HostSkillsLoadInput` to distinguish the host implementation from other skill
  providers.
- Keep shared loading primitives and skill outcome modeling in
  `codex-core-skills`.

GitOrigin-RevId: d81a21791d2ef8c066e157e7e538b8cb7ee4c24b

codex-rs/core/src/session/session.rs

@@ -461,7 +461,7 @@ pub(crate) struct AppServerClientMetadata {
 async fn warm_plugins_and_skills_for_session_init(
     config: Arc<Config>,
     plugins_manager: Arc<PluginsManager>,
-    skills_service: Arc<SkillsService>,
+    skills_service: Arc<HostSkillsService>,
     turn_environments: &TurnEnvironmentSnapshot,
 ) -> Vec<SkillError> {
     let fs = turn_environments.primary_filesystem();
@@ -510,7 +510,7 @@ impl Session {
         mut initial_history: InitialHistory,
         fork_persistence: ForkPersistence,
         session_source: SessionSource,
-        skills_service: Arc<SkillsService>,
+        skills_service: Arc<HostSkillsService>,
         plugins_manager: Arc<PluginsManager>,
         mcp_manager: Arc<McpManager>,
         code_mode_session_provider: Arc<dyn codex_code_mode::CodeModeSessionProvider>,