Canonicalize default tools under the functions namespace (#37022)

## What changed

- Group top-level function and custom tool definitions into a single `functions` namespace for Responses Lite providers that support namespaced tools.
- Normalize missing, empty, and explicit `functions` namespaces to the same tool identity across registration, routing, lifecycle hooks, configuration, and tool search.
- Keep default tool names unprefixed in code mode, display output, and dispatch traces while preserving explicit non-default namespaces.

## Testing

- Add coverage for Responses Lite serialization, tool search results, namespace normalization and collision handling, routing, lifecycle events, and code-mode namespace policies.

GitOrigin-RevId: d48414005b5d22d39b11a198e19c47814d3a19f2

codex-rs/ext/goal/src/extension.rs

@@ -372,7 +372,7 @@ where
             };
             let should_count_for_goal_progress = runtime.is_enabled()
                 && tool_attempt_counts_for_goal_progress(input.outcome)
-                && !(input.tool_name.namespace.is_none()
+                && !(input.tool_name.is_default_namespace()
                     && input.tool_name.name == UPDATE_GOAL_TOOL_NAME);
             if !should_count_for_goal_progress {
                 return;