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.

Author: jif-oai

codex-rs/analytics/src/analytics_client_tests.rs

@@ -128,6 +128,7 @@ fn sample_thread_with_metadata(
 ) -> Thread {
     Thread {
         id: thread_id.to_string(),
+        session_id: format!("session-{thread_id}"),
         forked_from_id: None,
         preview: "first prompt".to_string(),
         ephemeral,
@@ -154,7 +155,6 @@ fn sample_thread_start_response(
     model: &str,
 ) -> ClientResponsePayload {
     ClientResponsePayload::ThreadStart(ThreadStartResponse {
-        session_id: format!("session-{thread_id}"),
         thread: sample_thread_with_metadata(
             thread_id,
             ephemeral,
@@ -216,7 +216,6 @@ fn sample_thread_resume_response_with_source(
     thread_source: Option<AppServerThreadSource>,
 ) -> ClientResponsePayload {
     ClientResponsePayload::ThreadResume(ThreadResumeResponse {
-        session_id: format!("session-{thread_id}"),
         thread: sample_thread_with_metadata(thread_id, ephemeral, source, thread_source),
         model: model.to_string(),
         model_provider: "openai".to_string(),

codex-rs/analytics/src/client_tests.rs

@@ -76,6 +76,7 @@ fn sample_thread_archive_request() -> ClientRequest {
 fn sample_thread(thread_id: &str) -> Thread {
     Thread {
         id: thread_id.to_string(),
+        session_id: format!("session-{thread_id}"),
         forked_from_id: None,
         preview: "first prompt".to_string(),
         ephemeral: false,
@@ -102,7 +103,6 @@ fn sample_permission_profile() -> AppServerPermissionProfile {
 
 fn sample_thread_start_response() -> ClientResponsePayload {
     ClientResponsePayload::ThreadStart(ThreadStartResponse {
-        session_id: "session-1".to_string(),
         thread: sample_thread("thread-1"),
         model: "gpt-5".to_string(),
         model_provider: "openai".to_string(),
@@ -120,7 +120,6 @@ fn sample_thread_start_response() -> ClientResponsePayload {
 
 fn sample_thread_resume_response() -> ClientResponsePayload {
     ClientResponsePayload::ThreadResume(ThreadResumeResponse {
-        session_id: "session-2".to_string(),
         thread: sample_thread("thread-2"),
         model: "gpt-5".to_string(),
         model_provider: "openai".to_string(),
@@ -138,7 +137,6 @@ fn sample_thread_resume_response() -> ClientResponsePayload {
 
 fn sample_thread_fork_response() -> ClientResponsePayload {
     ClientResponsePayload::ThreadFork(ThreadForkResponse {
-        session_id: "session-3".to_string(),
         thread: sample_thread("thread-3"),
         model: "gpt-5".to_string(),
         model_provider: "openai".to_string(),