story-kit: done 240_story_btw_side_question_slash_command

Implement /btw side question slash command — lets users ask quick
questions from conversation context without disrupting the main chat.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

server/src/http/ws.rs

@@ -35,6 +35,14 @@ enum WsRequest {
     /// Heartbeat ping from the client. The server responds with `Pong` so the
     /// client can detect stale (half-closed) connections.
     Ping,
+    /// A quick side question answered from current conversation context.
+    /// The question and response are NOT added to the conversation history
+    /// and no tool calls are made.
+    SideQuestion {
+        question: String,
+        context_messages: Vec<Message>,
+        config: chat::ProviderConfig,
+    },
 }
 
 #[derive(Serialize)]
@@ -116,6 +124,14 @@ enum WsResponse {
     OnboardingStatus {
         needs_onboarding: bool,
     },
+    /// Streaming token from a `/btw` side question response.
+    SideQuestionToken {
+        content: String,
+    },
+    /// Final signal that the `/btw` side question has been fully answered.
+    SideQuestionDone {
+        response: String,
+    },
 }
 
 impl From<WatcherEvent> for Option<WsResponse> {
@@ -344,6 +360,33 @@ pub async fn ws_handler(ws: WebSocket, ctx: Data<&Arc<AppContext>>) -> impl poem
                                     Ok(WsRequest::Ping) => {
                                         let _ = tx.send(WsResponse::Pong);
                                     }
+                                    Ok(WsRequest::SideQuestion { question, context_messages, config }) => {
+                                        let tx_side = tx.clone();
+                                        let store = ctx.store.clone();
+                                        tokio::spawn(async move {
+                                            let result = chat::side_question(
+                                                context_messages,
+                                                question,
+                                                config,
+                                                store.as_ref(),
+                                                |token| {
+                                                    let _ = tx_side.send(WsResponse::SideQuestionToken {
+                                                        content: token.to_string(),
+                                                    });
+                                                },
+                                            ).await;
+                                            match result {
+                                                Ok(response) => {
+                                                    let _ = tx_side.send(WsResponse::SideQuestionDone { response });
+                                                }
+                                                Err(err) => {
+                                                    let _ = tx_side.send(WsResponse::SideQuestionDone {
+                                                        response: format!("Error: {err}"),
+                                                    });
+                                                }
+                                            }
+                                        });
+                                    }
                                     _ => {}
                                 }
                             }
@@ -370,6 +413,39 @@ pub async fn ws_handler(ws: WebSocket, ctx: Data<&Arc<AppContext>>) -> impl poem
                 Ok(WsRequest::PermissionResponse { .. }) => {
                     // Permission responses outside an active chat are ignored.
                 }
+                Ok(WsRequest::SideQuestion {
+                    question,
+                    context_messages,
+                    config,
+                }) => {
+                    let tx_side = tx.clone();
+                    let store = ctx.store.clone();
+                    tokio::spawn(async move {
+                        let result = chat::side_question(
+                            context_messages,
+                            question,
+                            config,
+                            store.as_ref(),
+                            |token| {
+                                let _ = tx_side.send(WsResponse::SideQuestionToken {
+                                    content: token.to_string(),
+                                });
+                            },
+                        )
+                        .await;
+                        match result {
+                            Ok(response) => {
+                                let _ = tx_side
+                                    .send(WsResponse::SideQuestionDone { response });
+                            }
+                            Err(err) => {
+                                let _ = tx_side.send(WsResponse::SideQuestionDone {
+                                    response: format!("Error: {err}"),
+                                });
+                            }
+                        }
+                    });
+                }
                 Err(err) => {
                     let _ = tx.send(WsResponse::Error {
                         message: format!("Invalid request: {err}"),