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