attribute subagent output to the task that spawned it

the harness stamps every message a subagent produces with parent_tool_use_id.
the sidecar wrote it outgoing and nothing ever read it coming back, so a
subagent's prose and tool calls were spliced into the main transcript as if the
agent you are talking to had produced them — and worse, its deltas were appended
to the same text buffer, so two voices were concatenated inside one bubble.

both buffering layers (stream-parser's textBuffer and turn-stream's buffer) are
now maps keyed by parent, and parentToolUseId rides on ChatEvent, ServerMessage
and Message. useChat nests parented output under the Task row that spawned it;
ToolActivity draws the trace inside the expanded panel.

background tasks get the same treatment from the other end: task:started and
task:notification were two unrelated fake assistant bubbles minutes apart, and
are now one role:'task' row correlated by taskId that appears pending and
resolves in place.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

src/servers/api/chat/websocket.ts

@@ -164,13 +164,23 @@ export function close(ws: ServerWebSocket<WSData>): void {
 function foldIntoSession(session: UserSession, msg: TurnMessage, model: string): void {
   switch (msg.type) {
     case 'assistant:delta':
-      session.streamBuffer += msg.text;
+      // A subagent's deltas are not the main agent typing; appending them here spliced its sentences into
+      // whatever the agent you are talking to was mid-way through saying.
+      if (!msg.parentToolUseId) session.streamBuffer += msg.text;
       break;
 
     case 'assistant:text':
-      session.messages.push({ id: randomUUID(), timestamp: Date.now(), role: 'assistant', text: msg.text, model });
+      session.messages.push({
+        id: randomUUID(),
+        timestamp: Date.now(),
+        role: 'assistant',
+        text: msg.text,
+        model,
+        parentToolUseId: msg.parentToolUseId,
+      });
       session.meta.messageCount += 1;
-      session.streamBuffer = '';
+      // Only the main agent's own stream feeds the buffer a resume replays as `streamingText`.
+      if (!msg.parentToolUseId) session.streamBuffer = '';
       break;
 
     case 'tool:start':
@@ -181,6 +191,7 @@ function foldIntoSession(session: UserSession, msg: TurnMessage, model: string):
         toolCallId: msg.toolCallId,
         toolName: msg.toolName,
         toolInput: msg.toolInput,
+        parentToolUseId: msg.parentToolUseId,
       });
       session.meta.messageCount += 1;
       break;
@@ -203,7 +214,8 @@ function foldIntoSession(session: UserSession, msg: TurnMessage, model: string):
       session.meta.cost.totalUSD += msg.cost.totalUSD;
       session.meta.updatedAt = Date.now();
       // The turn's cost belongs to the assistant message it paid for (as it did when officer built these).
-      const last = session.messages[session.messages.length - 1];
+      // The turn's cost is the main agent's, so skip past any subagent tail.
+      const last = [...session.messages].reverse().find((m) => !m.parentToolUseId);
       if (last?.role === 'assistant' && !last.cost) last.cost = msg.cost;
       break;
     }