feat: add session_id (#20437)

## Summary

Related to
https://openai.slack.com/archives/C095U48JNL9/p1777537279707449
TLDR:
We update the meaning of session ids and thread ids:
* thread_id stays as now
* session_id become a shared id between every thread under a /root
thread (i.e. every sub-agent share the same session id)

This PR introduces an explicit `SessionId` and threads it through the
protocol/client boundary so `session_id` and `thread_id` can diverge
when they need to, while preserving compatibility for older serialized
`session_configured` events.

---------

Co-authored-by: Codex <noreply@openai.com>

codex-rs/app-server/src/request_processors/thread_processor.rs

@@ -1148,6 +1148,7 @@ impl ThreadRequestProcessor {
             thread_response_active_permission_profile(config_snapshot.active_permission_profile);
 
         let response = ThreadStartResponse {
+            session_id: session_configured.session_id.to_string(),
             thread: thread.clone(),
             model: config_snapshot.model,
             model_provider: config_snapshot.model_provider_id,
@@ -2476,6 +2477,7 @@ impl ThreadRequestProcessor {
                 );
 
                 let response = ThreadResumeResponse {
+                    session_id: session_configured.session_id.to_string(),
                     thread,
                     model: session_configured.model,
                     model_provider: session_configured.model_provider_id,