fix(background-task): retry transient missing output tasks

Ultraworked with [Sisyphus](https://github.com/code-yeongyu/oh-my-openagent)

Co-authored-by: Sisyphus <clio-agent@sisyphuslabs.ai>

src/tools/background-task/create-background-output.blocking.test.ts

@@ -52,6 +52,47 @@ function createMockClient(): BackgroundOutputClient {
 }
 
 describe("createBackgroundOutput block=true polling", () => {
+  test("retries a missing background task id before reporting not found", async () => {
+    // #given
+    let lookupCount = 0
+    const task = createTask({
+      id: "bg_retry_visible",
+      status: "completed",
+      sessionId: "ses-retry-visible",
+    })
+    const manager: BackgroundOutputManager = {
+      getTask: (id: string) => {
+        if (id !== task.id) return undefined
+        lookupCount += 1
+        return lookupCount === 1 ? undefined : task
+      },
+    }
+    const client: BackgroundOutputClient = {
+      session: {
+        messages: async () => ({
+          data: [
+            {
+              id: "m1",
+              info: { role: "assistant", time: "2026-01-01T00:00:00Z" },
+              parts: [{ type: "text", text: "visible result" }],
+            },
+          ],
+        }),
+      },
+    }
+
+    const tool = createBackgroundOutput(manager, client)
+
+    // #when
+    const output = await tool.execute({ task_id: task.id }, mockContext)
+
+    // #then
+    expect(lookupCount).toBe(2)
+    expect(output).toContain("Task Result")
+    expect(output).toContain("visible result")
+    expect(output).not.toContain("Task not found")
+  })
+
   test("returns terminal error output when task fails during blocking wait", async () => {
     // #given
     let pollCount = 0