fix: add missing run_in_background to resume snippet and fix background launch detection

src/hooks/task-resume-info/index.test.ts

@@ -1,3 +1,5 @@
+/// <reference types="bun-types" />
+
 import { describe, it, expect } from "bun:test"
 import { createTaskResumeInfoHook } from "./index"
 
@@ -60,6 +62,19 @@ describe("createTaskResumeInfoHook", () => {
         expect(output.output).toContain("to continue:")
         expect(output.output).toContain("ses_abc123")
       })
+
+      it("#then should include run_in_background in resume info", async () => {
+        const input = createInput("call_omo_agent")
+        const output = {
+          title: "delegate_task",
+          output: "Task completed.\nSession ID: ses_abc123",
+          metadata: {},
+        }
+
+        await afterHook(input, output)
+
+        expect(output.output).toContain("run_in_background=false")
+      })
     })
   })