fix(claude): keep a background subagent's card labeled after its child streams (#6067)

Claude Code answers a background Agent call right away, then streams the
child's frames. Each frame re-emitted the parent's card from the sidechain
tracker after the tool-input cache had dropped the call, replacing the
settled, labeled card with a bare running "Task". The tracker now emits the
parent card only while the parent's tool call is still open.

Closes #6059

Co-authored-by: paseo-bot[bot] <266920839+paseo-bot[bot]@users.noreply.github.com>

packages/server/src/server/agent/providers/claude/agent.background-subagent.test.ts

@@ -314,6 +314,127 @@ describe("background Claude subagents", () => {
     });
   });
 
+  test("keeps the Task card labeled when the child's frames arrive after its launch result", async () => {
+    // Claude Code answers a background Agent call at once ("Agent launched") and only then streams
+    // the child's frames, so they arrive after the parent's tool call has its result.
+    queryFactory.mockImplementation(() =>
+      buildQueryMock([
+        { type: "system", subtype: "init", session_id: "bg-session", permissionMode: "default" },
+        {
+          type: "assistant",
+          message: {
+            model: "claude-haiku-4-5",
+            content: [
+              {
+                type: "tool_use",
+                id: "toolu_background",
+                name: "Agent",
+                input: {
+                  subagent_type: "general-purpose",
+                  description: "Count files here",
+                  prompt: "Run ls and reply with the number of entries.",
+                },
+              },
+            ],
+          },
+        },
+        {
+          type: "system",
+          subtype: "task_started",
+          task_id: "bg-task",
+          tool_use_id: "toolu_background",
+          task_type: "local_agent",
+          subagent_type: "general-purpose",
+          description: "Count files here",
+          prompt: "Run ls and reply with the number of entries.",
+        },
+        {
+          type: "user",
+          message: {
+            role: "user",
+            content: [
+              {
+                type: "tool_result",
+                tool_use_id: "toolu_background",
+                content: "Async agent launched successfully.",
+              },
+            ],
+          },
+        },
+        {
+          type: "assistant",
+          parent_tool_use_id: "toolu_background",
+          message: {
+            model: "claude-haiku-4-5",
+            content: [
+              {
+                type: "tool_use",
+                id: "toolu_ls",
+                name: "Bash",
+                input: { command: "ls -1", description: "List files" },
+              },
+            ],
+          },
+        },
+        {
+          type: "user",
+          parent_tool_use_id: "toolu_background",
+          message: {
+            role: "user",
+            content: [{ type: "tool_result", tool_use_id: "toolu_ls", content: "a\nb\nc" }],
+          },
+        },
+        {
+          type: "assistant",
+          parent_tool_use_id: "toolu_background",
+          message: { model: "claude-haiku-4-5", content: [{ type: "text", text: "3" }] },
+        },
+        {
+          type: "system",
+          subtype: "task_updated",
+          task_id: "bg-task",
+          patch: { status: "completed" },
+        },
+        {
+          type: "system",
+          subtype: "task_notification",
+          task_id: "bg-task",
+          tool_use_id: "toolu_background",
+          status: "completed",
+        },
+        { type: "result", subtype: "success", usage: {}, total_cost_usd: 0 },
+      ]),
+    );
+    const session = await new ClaudeAgentClient({
+      logger: createTestLogger(),
+      queryFactory,
+      resolveBinary: async () => "/test/claude/bin",
+    }).createSession({ provider: "claude", cwd: process.cwd() });
+    const events = await collectUntilTerminal(streamSession(session, "delegate work"));
+    await session.close();
+
+    const rows: AgentTimelineRow[] = events
+      .filter((event) => event.type === "timeline")
+      .map((event, index) => ({
+        seq: index + 1,
+        timestamp: new Date(Date.UTC(2026, 9, 4, 0, 0, index)).toISOString(),
+        item: event.item,
+      }));
+    const cards = projectTimelineRows({ rows, mode: "projected" })
+      .map((entry) => entry.item)
+      .filter((item) => item.type === "tool_call" && item.callId === "toolu_background");
+
+    expect(cards).toHaveLength(1);
+    expect(cards[0]).toMatchObject({
+      status: "completed",
+      detail: {
+        type: "sub_agent",
+        subAgentType: "general-purpose",
+        description: "Count files here",
+      },
+    });
+  });
+
   test.each([
     {
       source: "system task protocol",

packages/server/src/server/agent/providers/claude/agent.ts

@@ -2092,7 +2092,11 @@ class ClaudeAgentSession implements AgentSession {
     // identity and status from frames for them. Detecting the capability beats comparing version
     // strings: it reacts to what this session actually does.
     isDescriptorOwnedElsewhere: () => this.taskProtocolSource.isActive,
+    // The parent's tool call owns its card once its result arrives. A background child streams
+    // its frames after Claude has already answered the call, and re-emitting the card from them
+    // would replace the settled card with an unlabeled, running one.
     needsSyntheticParentToolCard: (toolUseId) =>
+      this.toolUseCache.has(toolUseId) &&
       this.taskProtocolSource.needsSyntheticParentToolCard(toolUseId),
   });
   private persistedHistory: PersistedTimelineEntry[] = [];