notify: include client in legacy hook payload (#12968)

## Why

The `notify` hook payload did not identify which Codex client started
the turn. That meant downstream notification hooks could not distinguish
between completions coming from the TUI and completions coming from
app-server clients such as VS Code or Xcode. Now that the Codex App
provides its own desktop notifications, it would be nice to be able to
filter those out.

This change adds that context without changing the existing payload
shape for callers that do not know the client name, and keeps the new
end-to-end test cross-platform.

## What changed

- added an optional top-level `client` field to the legacy `notify` JSON
payload
- threaded that value through `core` and `hooks`; the internal session
and turn state now carries it as `app_server_client_name`
- set the field to `codex-tui` for TUI turns
- captured `initialize.clientInfo.name` in the app server and applied it
to subsequent turns before dispatching hooks
- replaced the notify integration test hook with a `python3` script so
the test does not rely on Unix shell permissions or `bash`
- documented the new field in `docs/config.md`

## Testing

- `cargo test -p codex-hooks`
- `cargo test -p codex-tui`
- `cargo test -p codex-app-server
suite::v2::initialize::turn_start_notify_payload_includes_initialize_client_name
-- --exact --nocapture`
- `cargo test -p codex-core` (`src/lib.rs` passed; `core/tests/all.rs`
still has unrelated existing failures in this environment)

## Docs

The public config reference on `developers.openai.com/codex` should
mention that the legacy `notify` payload may include a top-level
`client` field. The TUI reports `codex-tui`, and the app server reports
`initialize.clientInfo.name` when it is available.

codex-rs/app-server/src/codex_message_processor.rs

@@ -560,7 +560,12 @@ impl CodexMessageProcessor {
         Ok((review_request, hint))
     }
 
-    pub async fn process_request(&mut self, connection_id: ConnectionId, request: ClientRequest) {
+    pub async fn process_request(
+        &mut self,
+        connection_id: ConnectionId,
+        request: ClientRequest,
+        app_server_client_name: Option<String>,
+    ) {
         let to_connection_request_id = |request_id| ConnectionRequestId {
             connection_id,
             request_id,
@@ -647,8 +652,12 @@ impl CodexMessageProcessor {
                     .await;
             }
             ClientRequest::TurnStart { request_id, params } => {
-                self.turn_start(to_connection_request_id(request_id), params)
-                    .await;
+                self.turn_start(
+                    to_connection_request_id(request_id),
+                    params,
+                    app_server_client_name.clone(),
+                )
+                .await;
             }
             ClientRequest::TurnSteer { request_id, params } => {
                 self.turn_steer(to_connection_request_id(request_id), params)
@@ -767,12 +776,20 @@ impl CodexMessageProcessor {
                     .await;
             }
             ClientRequest::SendUserMessage { request_id, params } => {
-                self.send_user_message(to_connection_request_id(request_id), params)
-                    .await;
+                self.send_user_message(
+                    to_connection_request_id(request_id),
+                    params,
+                    app_server_client_name.clone(),
+                )
+                .await;
             }
             ClientRequest::SendUserTurn { request_id, params } => {
-                self.send_user_turn(to_connection_request_id(request_id), params)
-                    .await;
+                self.send_user_turn(
+                    to_connection_request_id(request_id),
+                    params,
+                    app_server_client_name.clone(),
+                )
+                .await;
             }
             ClientRequest::InterruptConversation { request_id, params } => {
                 self.interrupt_conversation(to_connection_request_id(request_id), params)
@@ -5063,6 +5080,7 @@ impl CodexMessageProcessor {
         &self,
         request_id: ConnectionRequestId,
         params: SendUserMessageParams,
+        app_server_client_name: Option<String>,
     ) {
         let SendUserMessageParams {
             conversation_id,
@@ -5081,6 +5099,12 @@ impl CodexMessageProcessor {
             self.outgoing.send_error(request_id, error).await;
             return;
         };
+        if let Err(error) =
+            Self::set_app_server_client_name(conversation.as_ref(), app_server_client_name).await
+        {
+            self.outgoing.send_error(request_id, error).await;
+            return;
+        }
 
         let mapped_items: Vec<CoreInputItem> = items
             .into_iter()
@@ -5111,7 +5135,12 @@ impl CodexMessageProcessor {
             .await;
     }
 
-    async fn send_user_turn(&self, request_id: ConnectionRequestId, params: SendUserTurnParams) {
+    async fn send_user_turn(
+        &self,
+        request_id: ConnectionRequestId,
+        params: SendUserTurnParams,
+        app_server_client_name: Option<String>,
+    ) {
         let SendUserTurnParams {
             conversation_id,
             items,
@@ -5137,6 +5166,12 @@ impl CodexMessageProcessor {
             self.outgoing.send_error(request_id, error).await;
             return;
         };
+        if let Err(error) =
+            Self::set_app_server_client_name(conversation.as_ref(), app_server_client_name).await
+        {
+            self.outgoing.send_error(request_id, error).await;
+            return;
+        }
 
         let mapped_items: Vec<CoreInputItem> = items
             .into_iter()
@@ -5638,7 +5673,12 @@ impl CodexMessageProcessor {
         let _ = conversation.submit(Op::Interrupt).await;
     }
 
-    async fn turn_start(&self, request_id: ConnectionRequestId, params: TurnStartParams) {
+    async fn turn_start(
+        &self,
+        request_id: ConnectionRequestId,
+        params: TurnStartParams,
+        app_server_client_name: Option<String>,
+    ) {
         if let Err(error) = Self::validate_v2_input_limit(&params.input) {
             self.outgoing.send_error(request_id, error).await;
             return;
@@ -5650,6 +5690,12 @@ impl CodexMessageProcessor {
                 return;
             }
         };
+        if let Err(error) =
+            Self::set_app_server_client_name(thread.as_ref(), app_server_client_name).await
+        {
+            self.outgoing.send_error(request_id, error).await;
+            return;
+        }
 
         let collaboration_modes_config = CollaborationModesConfig {
             default_mode_request_user_input: thread.enabled(Feature::DefaultModeRequestUserInput),
@@ -5731,6 +5777,20 @@ impl CodexMessageProcessor {
         }
     }
 
+    async fn set_app_server_client_name(
+        thread: &CodexThread,
+        app_server_client_name: Option<String>,
+    ) -> Result<(), JSONRPCErrorError> {
+        thread
+            .set_app_server_client_name(app_server_client_name)
+            .await
+            .map_err(|err| JSONRPCErrorError {
+                code: INTERNAL_ERROR_CODE,
+                message: format!("failed to set app server client name: {err}"),
+                data: None,
+            })
+    }
+
     async fn turn_steer(&self, request_id: ConnectionRequestId, params: TurnSteerParams) {
         let (_, thread) = match self.load_thread(&params.thread_id).await {
             Ok(v) => v,