Allow injecting the Codex Apps tools cache (#33113)

## What changed

- Accept a caller-provided `CodexAppsToolsCache` when constructing a `ThreadManager` and pass it through to the MCP manager.
- Add `ConnectorRuntimeManager::new_without_cache()` for an in-memory runtime that neither loads nor persists connector state on disk.
- Re-export `CodexAppsToolsCache` from `codex-core` and `codex-core-api` for embedders.

## Testing

- Verify that a cache-disabled connector runtime ignores existing disk state and publishes live tools without creating cache files.

GitOrigin-RevId: f52f4f27c425a8d84ad0d0987b30a6fc3c14d702

codex-rs/core/src/mcp.rs

@@ -58,6 +58,7 @@ impl McpManager {
         Self::new_with_extensions(
             plugins_manager,
             codex_extension_api::empty_extension_registry(),
+            ConnectorRuntimeManager::default(),
         )
     }
 
@@ -65,11 +66,12 @@ impl McpManager {
     pub fn new_with_extensions(
         plugins_manager: Arc<PluginsManager>,
         extensions: Arc<ExtensionRegistry<Config>>,
+        codex_apps_tools_cache: ConnectorRuntimeManager<ToolInfo>,
     ) -> Self {
         Self {
             plugins_manager,
             extensions,
-            codex_apps_tools_cache: ConnectorRuntimeManager::default(),
+            codex_apps_tools_cache,
         }
     }