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-protocol/src/protocol/common.rs

@@ -2176,6 +2176,7 @@ mod tests {
         let response = ClientResponse::ThreadStart {
             request_id: RequestId::Integer(7),
             response: v2::ThreadStartResponse {
+                session_id: "67e55044-10b1-426f-9247-bb680e5fe0c7".to_string(),
                 thread: v2::Thread {
                     id: "67e55044-10b1-426f-9247-bb680e5fe0c8".to_string(),
                     forked_from_id: None,
@@ -2217,6 +2218,7 @@ mod tests {
                 "method": "thread/start",
                 "id": 7,
                 "response": {
+                    "sessionId": "67e55044-10b1-426f-9247-bb680e5fe0c7",
                     "thread": {
                         "id": "67e55044-10b1-426f-9247-bb680e5fe0c8",
                         "forkedFromId": null,

codex-rs/app-server-protocol/src/protocol/v2/thread.rs

@@ -189,6 +189,9 @@ pub struct MockExperimentalMethodResponse {
 #[serde(rename_all = "camelCase")]
 #[ts(export_to = "v2/")]
 pub struct ThreadStartResponse {
+    /// Session id shared by threads that belong to the same session tree.
+    #[serde(default)]
+    pub session_id: String,
     pub thread: Thread,
     pub model: String,
     pub model_provider: String,
@@ -304,6 +307,9 @@ pub struct ThreadResumeParams {
 #[serde(rename_all = "camelCase")]
 #[ts(export_to = "v2/")]
 pub struct ThreadResumeResponse {
+    /// Session id shared by threads that belong to the same session tree.
+    #[serde(default)]
+    pub session_id: String,
     pub thread: Thread,
     pub model: String,
     pub model_provider: String,