clean models manager (#9168)

Have only the following Methods:
- `list_models`: getting current available models
- `try_list_models`: sync version no refresh for tui use
- `get_default_model`: get the default model (should be tightened to
core and received on session configuration)
- `get_model_info`: get `ModelInfo` for a specific model (should be
tightened to core but used in tests)
- `refresh_if_new_etag`: trigger refresh on different etags

Also move the cache to its own struct

codex-rs/app-server/src/models.rs

@@ -4,12 +4,13 @@ use codex_app_server_protocol::Model;
 use codex_app_server_protocol::ReasoningEffortOption;
 use codex_core::ThreadManager;
 use codex_core::config::Config;
+use codex_core::models_manager::manager::RefreshStrategy;
 use codex_protocol::openai_models::ModelPreset;
 use codex_protocol::openai_models::ReasoningEffortPreset;
 
 pub async fn supported_models(thread_manager: Arc<ThreadManager>, config: &Config) -> Vec<Model> {
     thread_manager
-        .list_models(config)
+        .list_models(config, RefreshStrategy::OnlineIfUncached)
         .await
         .into_iter()
         .filter(|preset| preset.show_in_picker)