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/thread-manager-sample/src/main.rs

@@ -16,6 +16,7 @@ use codex_core_api::AskForApproval;
 use codex_core_api::AuthCredentialsStoreMode;
 use codex_core_api::AuthManager;
 use codex_core_api::AutoCompactTokenLimitScope;
+use codex_core_api::CodexAppsToolsCache;
 use codex_core_api::CodexHomeUserInstructionsProvider;
 use codex_core_api::CodexThread;
 use codex_core_api::Config;
@@ -135,6 +136,7 @@ async fn run_main(arg0_paths: Arg0DispatchPaths) -> anyhow::Result<()> {
         &config,
         Arc::clone(&auth_manager),
         build_models_manager(&config, auth_manager),
+        CodexAppsToolsCache::default(),
         SessionSource::Exec,
         environment_manager,
         Arc::new(extensions.build()),