Surface cross-workspace subagents in their workspaces (#2061)

* fix(workspaces): show provider subagent activity

Provider subagent lifecycle lives outside managed agent snapshots, so workspace aggregation dropped it after the parent turn finished. Count running provider subagents against the delegation root and emit workspace updates when their status changes.

* fix(workspaces): surface cross-workspace subagents

packages/app/e2e/helpers/subagents.ts

@@ -14,6 +14,17 @@ export interface SeededSubagentPair {
   workspaceId: string;
 }
 
+export interface SeededCrossWorkspaceSubagentPair {
+  parent: {
+    id: string;
+    workspaceId: string;
+  };
+  child: {
+    id: string;
+    workspaceId: string;
+  };
+}
+
 export async function seedParentWithSubagent(
   workspace: Pick<SeededWorkspace, "client" | "repoPath" | "workspaceId">,
   input: { parentTitle: string; childTitle: string },
@@ -51,6 +62,60 @@ export async function seedParentWithSubagent(
   };
 }
 
+export async function seedParentWithCrossWorkspaceSubagent(
+  workspace: Pick<SeededWorkspace, "client" | "repoPath" | "workspaceId" | "projectId">,
+  input: { parentTitle: string; childTitle: string },
+): Promise<SeededCrossWorkspaceSubagentPair> {
+  const parent = await workspace.client.createAgent({
+    provider: "mock",
+    cwd: workspace.repoPath,
+    workspaceId: workspace.workspaceId,
+    title: input.parentTitle,
+    modeId: "load-test",
+    model: "ten-second-stream",
+  });
+  const createdWorkspace = await workspace.client.createWorkspace({
+    source: {
+      kind: "directory",
+      path: workspace.repoPath,
+      projectId: workspace.projectId,
+    },
+    title: "Subagent workspace",
+  });
+  if (!createdWorkspace.workspace) {
+    throw new Error(createdWorkspace.error ?? "Failed to create subagent workspace");
+  }
+
+  const child = await workspace.client.createAgent({
+    provider: "mock",
+    cwd: workspace.repoPath,
+    workspaceId: createdWorkspace.workspace.id,
+    title: input.childTitle,
+    modeId: "load-test",
+    model: "five-minute-stream",
+    initialPrompt: "stay running",
+    labels: {
+      [PARENT_AGENT_ID_LABEL]: parent.id,
+    },
+  });
+  await workspace.client.waitForAgentUpsert(
+    child.id,
+    (snapshot) => snapshot.status === "running",
+    15_000,
+  );
+
+  return {
+    parent: {
+      id: parent.id,
+      workspaceId: workspace.workspaceId,
+    },
+    child: {
+      id: child.id,
+      workspaceId: createdWorkspace.workspace.id,
+    },
+  };
+}
+
 export async function openSubagentsTrack(page: Page): Promise<void> {
   await page.getByTestId("subagents-track-header").click();
 }