feat(app-server): move v2 sessionId onto Thread (#21336)

## Why

`session_id` and `thread_id` are separate identities after #20437, but
app-server only surfaced `sessionId` on the `thread/start`,
`thread/resume`, and `thread/fork` response envelopes. Other
thread-bearing surfaces such as `thread/list`, `thread/read`,
`thread/started`, `thread/rollback`, `thread/metadata/update`, and
`thread/unarchive` either lacked the grouping key or forced clients to
special-case those three responses.

Making `sessionId` part of the reusable `Thread` payload gives every v2
API surface one place to expose session-tree identity.

## Mental model
  1. thread.sessionId lives on `Thread`
2. It is a view/runtime identity for the current live session tree, not
durable stored lineage metadata
3. When app-server has a live loaded thread, it copies the real value
from core’s session_configured.session_id
4. When it only has stored/unloaded data, it falls back to
thread.sessionId = thread.id

## What changed

- Added `sessionId` to the v2
[`Thread`](https://github.com/openai/codex/blob/8fc9e9b4cf81b6f61d432e71f1eb266f6f104b63/codex-rs/app-server-protocol/src/protocol/v2/thread_data.rs#L105-L109).
- Removed the duplicate top-level `sessionId` fields from
`thread/start`, `thread/resume`, and `thread/fork`; clients should now
read `response.thread.sessionId`.
- Populated `thread.sessionId` when building live thread responses,
replaying loaded threads, and returning stored-thread summaries so the
field is present across start, resume, fork, list, read, rollback,
metadata-update, unarchive, and `thread/started` paths. See
[`load_thread_from_resume_source_or_send_internal`](https://github.com/openai/codex/blob/8fc9e9b4cf81b6f61d432e71f1eb266f6f104b63/codex-rs/app-server/src/request_processors/thread_processor.rs#L2824-L2918)
and
[`thread_from_stored_thread`](https://github.com/openai/codex/blob/8fc9e9b4cf81b6f61d432e71f1eb266f6f104b63/codex-rs/app-server/src/request_processors/thread_processor.rs#L3671-L3719).
- Preserved the stored-thread fallback: if a thread has not been loaded
into a live session tree yet, `thread.sessionId` falls back to
`thread.id`; once the thread is live again, the field reports the active
session tree root.
- Regenerated the JSON/TypeScript schemas and updated the app-server
README examples to show
[`thread.sessionId`](https://github.com/openai/codex/blob/8fc9e9b4cf81b6f61d432e71f1eb266f6f104b63/codex-rs/app-server/README.md#L306-L310)
on the thread object.

codex-rs/app-server-protocol/src/protocol/common.rs

@@ -2176,9 +2176,9 @@ 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(),
+                    session_id: "67e55044-10b1-426f-9247-bb680e5fe0c7".to_string(),
                     forked_from_id: None,
                     preview: "first prompt".to_string(),
                     ephemeral: true,
@@ -2218,9 +2218,9 @@ mod tests {
                 "method": "thread/start",
                 "id": 7,
                 "response": {
-                    "sessionId": "67e55044-10b1-426f-9247-bb680e5fe0c7",
                     "thread": {
                         "id": "67e55044-10b1-426f-9247-bb680e5fe0c8",
+                        "sessionId": "67e55044-10b1-426f-9247-bb680e5fe0c7",
                         "forkedFromId": null,
                         "preview": "first prompt",
                         "ephemeral": true,

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

@@ -3437,10 +3437,11 @@ fn thread_start_params_preserve_explicit_null_service_tier() {
 }
 
 #[test]
-fn thread_lifecycle_responses_default_missing_compat_fields() {
+fn thread_lifecycle_responses_default_missing_optional_fields() {
     let response = json!({
         "thread": {
             "id": "thread-id",
+            "sessionId": "thread-id",
             "forkedFromId": null,
             "preview": "",
             "ephemeral": false,

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

@@ -189,9 +189,6 @@ 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,
@@ -307,9 +304,6 @@ 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,
@@ -419,9 +413,6 @@ pub struct ThreadForkParams {
 #[serde(rename_all = "camelCase")]
 #[ts(export_to = "v2/")]
 pub struct ThreadForkResponse {
-    /// 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,

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

@@ -104,6 +104,8 @@ pub struct GitInfo {
 #[ts(export_to = "v2/")]
 pub struct Thread {
     pub id: String,
+    /// Session id shared by threads that belong to the same session tree.
+    pub session_id: String,
     /// Source thread id when this thread was created by forking another thread.
     pub forked_from_id: Option<String>,
     /// Usually the first user message in the thread, if available.