feat(analytics): generate an installation_id and pass it in responsesapi client_metadata (#16912)

## Summary

This adds a stable Codex installation ID and includes it on Responses
API requests via `x-codex-installation-id` passed in via the
`client_metadata` field for analytics/debugging.

The main pieces are:
- persist a UUID in `$CODEX_HOME/installation_id`
- thread the installation ID into `ModelClient`
- send it in `client_metadata` on Responses requests so it works
consistently across HTTP and WebSocket transports

codex-rs/codex-api/tests/clients.rs

@@ -278,6 +278,7 @@ async fn streaming_client_retries_on_transport_error() -> Result<()> {
         service_tier: None,
         prompt_cache_key: None,
         text: None,
+        client_metadata: None,
     };
     let client = ResponsesClient::new(transport.clone(), provider, NoAuth);
 
@@ -320,6 +321,7 @@ async fn azure_default_store_attaches_ids_and_headers() -> Result<()> {
         service_tier: None,
         prompt_cache_key: None,
         text: None,
+        client_metadata: None,
     };
 
     let mut extra_headers = HeaderMap::new();