Allow injecting the models manager into ThreadManager (#32911)

## Why

Embedding callers need to control whether model catalogs are persisted to disk.

## What changed

- Accept a shared models manager when constructing `ThreadManager` instead of always creating a cached manager internally.
- Add provider APIs for creating uncached model managers. OpenAI-compatible providers fetch on each `OnlineIfUncached` refresh without reading or writing `models_cache.json`.
- Keep existing app server, MCP server, sample, and test callers on the standard cached manager.

## Testing

- Verify an uncached manager fetches on every refresh.
- Verify an injected uncached manager controls thread refresh behavior and does not create `models_cache.json`.

GitOrigin-RevId: 8bb646054ecec4ccb865b2bf56249384916ea9db

codex-rs/core/src/tools/handlers/multi_agents_tests.rs

@@ -4293,9 +4293,11 @@ async fn tool_handlers_cascade_close_and_resume_and_keep_explicitly_closed_subtr
         .enable(Feature::Sqlite)
         .expect("test config should allow sqlite");
     let state_db = init_state_db(&config).await;
+    let auth_manager = AuthManager::from_auth_for_testing(CodexAuth::from_api_key("dummy"));
     let manager = ThreadManager::new(
         &config,
-        AuthManager::from_auth_for_testing(CodexAuth::from_api_key("dummy")),
+        auth_manager.clone(),
+        crate::thread_manager::build_models_manager(&config, auth_manager),
         SessionSource::Exec,
         Arc::new(codex_exec_server::EnvironmentManager::default_for_tests()),
         empty_extension_registry(),