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/lib.rs

@@ -65,6 +65,7 @@ pub use network_proxy_loader::MtimeConfigReloader;
 pub use network_proxy_loader::build_network_proxy_state;
 pub use network_proxy_loader::build_network_proxy_state_and_reloader;
 mod original_image_detail;
+pub use codex_mcp::CodexAppsToolsCache;
 pub use codex_mcp::SandboxState;
 mod mcp_openai_file;
 mod mcp_tool_call;