feat: return session ID from thread/fork (#21332)

## Why

`thread/start` and `thread/resume` already return `sessionId`, but
`thread/fork` only returned the new thread. That left clients to infer
the forked thread's session identity from `thread.id`, which kept the
new `session_id` / `thread_id` split implicit at one lifecycle boundary.
Follow-up to #20437.

## What changed

- Add `sessionId` to `ThreadForkResponse`.
- Populate it from the forked session configuration.
- Regenerate the v2 JSON/TypeScript schema fixtures and update the
app-server docs/example.
- Extend the fork integration test to assert the returned `sessionId`.

## Verification

- Added coverage in `thread_fork_creates_new_thread_and_emits_started`
for the new response field.

codex-rs/app-server-protocol/schema/json/codex_app_server_protocol.schemas.json

@@ -15664,6 +15664,11 @@
               }
             ]
           },
+          "sessionId": {
+            "default": "",
+            "description": "Session id shared by threads that belong to the same session tree.",
+            "type": "string"
+          },
           "thread": {
             "$ref": "#/definitions/v2/Thread"
           }

codex-rs/app-server-protocol/schema/json/codex_app_server_protocol.v2.schemas.json

@@ -13550,6 +13550,11 @@
             }
           ]
         },
+        "sessionId": {
+          "default": "",
+          "description": "Session id shared by threads that belong to the same session tree.",
+          "type": "string"
+        },
         "thread": {
           "$ref": "#/definitions/Thread"
         }

codex-rs/app-server-protocol/schema/json/v2/ThreadForkResponse.json

@@ -2619,6 +2619,11 @@
         }
       ]
     },
+    "sessionId": {
+      "default": "",
+      "description": "Session id shared by threads that belong to the same session tree.",
+      "type": "string"
+    },
     "thread": {
       "$ref": "#/definitions/Thread"
     }

codex-rs/app-server-protocol/schema/typescript/v2/ThreadForkResponse.ts

@@ -9,7 +9,10 @@ import type { AskForApproval } from "./AskForApproval";
 import type { SandboxPolicy } from "./SandboxPolicy";
 import type { Thread } from "./Thread";
 
-export type ThreadForkResponse = {thread: Thread, model: string, modelProvider: string, serviceTier: ServiceTier | null, cwd: AbsolutePathBuf, /**
+export type ThreadForkResponse = {/**
+ * Session id shared by threads that belong to the same session tree.
+ */
+sessionId: string, thread: Thread, model: string, modelProvider: string, serviceTier: ServiceTier | null, cwd: AbsolutePathBuf, /**
  * Instruction source files currently loaded for this thread.
  */
 instructionSources: Array<AbsolutePathBuf>, approvalPolicy: AskForApproval, /**