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/core/src/codex.rs

@@ -24,6 +24,7 @@ use crate::compact_remote::run_inline_remote_auto_compact_task;
 use crate::config::ManagedFeatures;
 use crate::connectors;
 use crate::exec_policy::ExecPolicyManager;
+use crate::installation_id::resolve_installation_id;
 use crate::parse_turn_item;
 use crate::path_utils::normalize_for_native_workdir;
 use crate::realtime_conversation::RealtimeConversationManager;
@@ -1927,6 +1928,7 @@ impl Session {
             });
         }
 
+        let installation_id = resolve_installation_id(&config.codex_home).await?;
         let services = SessionServices {
             // Initialize the MCP connection manager with an uninitialized
             // instance. It will be replaced with one created via
@@ -1970,6 +1972,7 @@ impl Session {
             model_client: ModelClient::new(
                 Some(Arc::clone(&auth_manager)),
                 conversation_id,
+                installation_id,
                 session_configuration.provider.clone(),
                 session_configuration.session_source.clone(),
                 config.model_verbosity,