Migrate tui to use models manager (#7555)

- This PR treats the `ModelsManager` like `AuthManager` and propagate it
into the tui, replacing the `builtin_model_presets`
- We are also decreasing the visibility of `builtin_model_presets`

based on https://github.com/openai/codex/pull/7552

codex-rs/tui/src/app_backtrack.rs

@@ -346,6 +346,7 @@ impl App {
             initial_images: Vec::new(),
             enhanced_keys_supported: self.enhanced_keys_supported,
             auth_manager: self.auth_manager.clone(),
+            models_manager: self.server.get_models_manager(),
             feedback: self.feedback.clone(),
             skills: self.skills.clone(),
             is_first_run: false,