chat: persistent Agent SDK session per chat — decouple worker from turn (Phase 1)

Root fix for orphaned background tasks: the platform drove Claude Code as a
one-shot `claude -p` per turn (stdin ignored, process exits at turn end), so
run_in_background/Monitor work — and its task_notification — had no live harness
to return to. Now each chat session runs ONE long-lived Agent SDK query() with
streaming input; turns are user messages pushed onto it, and the session stays
warm between turns.

- claude-manager: persistent `query({ prompt: AsyncIterable, options })` per
  sessionKey (bypassPermissions, --resume, mcp via extraArgs, CLAUDECODE stripped).
  Single consumer loop maps every SDK message → ChatEvent, incl. post-turn
  task_started / task_notification. interrupt() = stop-turn; abort() = kill-session;
  30-min idle GC.
- stream-parser: processMessage() (object-level, reused by the SDK loop) + task
  message handling. ChatEvent/ServerMessage gain task:started / task:notification.
- API: the sidecar event subscription is now SESSION-scoped (no longer unsubscribes
  on 'result'), so background events after turn-end still reach the client. First
  turn opens the session; later turns push onto it. handleStop → interrupt (keeps
  session warm); disconnect/deleteSession → kill.
- protocol/sidecar-registry/user-instance: claude:interrupt command + interruptClaude.
- client: render task:started / task:notification in the transcript.

Verified end-to-end through the real chat WS: a run_in_background task's completion
arrives ~6s AFTER the turn's result; multi-turn on one warm session works.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

src/servers/api/chat/websocket.ts

@@ -275,6 +275,18 @@ function createEventHandler(sessionId: string, model: string, cwd: string) {
         session.isGenerating = false;
         break;
       }
+
+      case 'task:started': {
+        // Background task launched (run_in_background / Monitor). Independent of turn state.
+        sendToClient(ws, { type: 'task:started', taskId: event.taskId, description: event.description, taskType: event.taskType });
+        break;
+      }
+
+      case 'task:notification': {
+        // Background task finished — arrives AFTER the turn's 'result'; the whole point of the fix.
+        sendToClient(ws, { type: 'task:notification', taskId: event.taskId, status: event.status, summary: event.summary });
+        break;
+      }
     }
   };
 }
@@ -372,21 +384,35 @@ async function handleClaudeCodeChat(
   const onEvent = createEventHandler(sessionId, model, cwd);
 
   try {
-    const handle = await sendClaudeCodeStreaming({
-      userId,
-      email,
-      username,
-      prompt: effectivePrompt,
-      sessionKey: sessionId,
-      cwd,
-      model,
-      resumeSessionId: msg.resumeSessionId,
-      onEvent,
-    });
-
-    // Store sentinel so handleStop can kill it via sidecar
-    session.piProcess = sessionId as any;
-    session._claudeKill = handle.kill;
+    if (!session._claudeKill) {
+      // First turn of this session: open the persistent session + a SESSION-scoped event subscription
+      // (survives turn-end so background task:notifications keep flowing). handle.kill tears both down.
+      const handle = await sendClaudeCodeStreaming({
+        userId,
+        email,
+        username,
+        prompt: effectivePrompt,
+        sessionKey: sessionId,
+        cwd,
+        model,
+        resumeSessionId: msg.resumeSessionId,
+        onEvent,
+      });
+      session.piProcess = sessionId as any;
+      session._claudeKill = handle.kill;
+    } else {
+      // Session already live: push this turn onto the existing persistent session (no new subscription).
+      await sidecar.spawnClaudeStreaming({
+        userId,
+        email,
+        username,
+        prompt: effectivePrompt,
+        sessionKey: sessionId,
+        cwd,
+        model,
+        resumeSessionId: msg.resumeSessionId,
+      });
+    }
   } catch (err) {
     logger.error('Failed to start Claude Code streaming', { sessionId, error: String(err) });
     sendToClient(ws, { type: 'error', message: 'Failed to start Claude Code' });
@@ -524,8 +550,10 @@ async function handleStop(ws: ServerWebSocket<WSData>): Promise<void> {
     if (session?.piProcess) {
       try {
         if (isClaudeModel(session.model)) {
-          sidecar.killClaude(sessionId, session.email);
-          logger.info('Killed Claude Code process via sidecar', { sessionId });
+          // Interrupt the current turn but KEEP the persistent session alive (background tasks + the
+          // warm worker survive). Full teardown is 'disconnect' → deleteSession → _claudeKill.
+          void sidecar.interruptClaude(sessionId, session.email);
+          logger.info('Interrupted Claude Code turn via sidecar (session stays warm)', { sessionId });
         } else {
           session._claudeKill?.(); // OpenCode: abort the turn via the stored handle
           logger.info('Aborted OpenCode turn', { sessionId });