test: defang two flaky tests on main CI

agent.integration "creates an autonomous live turn" — the prompt asked
Claude to use a `Task` tool that doesn't exist in the SDK (Paseo
synthesizes Task entries from sidechain notifications, but Claude can't
invoke it). Haiku non-deterministically refused or complied. Switch to
Bash with run_in_background, matching the deterministic
claude-autonomous-wake-simple.real.e2e variant — same autonomous-wake
mechanism is exercised.

schedule/service "defaults new-agent modeId to provider's unattended
mode" — afterEach raced AgentStorage's background snapshot persist,
producing intermittent ENOTEMPTY rmdirs. Drain pending writes with
agentStorage.flush() before rm.

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

@@ -378,9 +378,9 @@ describe("ClaudeAgentSession integration", () => {
         streamSession(
           handle.session,
           [
-            "Use the Task tool to start a background sub-agent.",
+            "Use the Bash tool with run_in_background.",
-            "In that task, run the Bash command exactly: sleep 3 && echo BACKGROUND_DONE",
+            "Run exactly: sleep 3",
-            "Do not wait for task completion.",
+            "Do not wait for the task result.",
             "Reply immediately with exactly: SPAWNED",
             `When the background task completes later, reply with exactly: ${autonomousWakeToken}`,
           ].join(" "),

packages/server/src/server/schedule/service.test.ts

@@ -27,6 +27,9 @@ describe("ScheduleService", () => {
   });
 
   afterEach(async () => {
+    // Drain pending background persists before deleting the dir to avoid
+    // ENOTEMPTY races when AgentManager flushes a snapshot mid-cleanup.
+    await agentStorage.flush();
     await rm(tempDir, { recursive: true, force: true });
   });