fix(sessions): leave a pending idle alert to the user through a keep-alive turn

Only a human spends an idle alert, but the keep-alive turn resolved an unseen one three ways: its working transition, its stop hook, and its own idle prompt replacing the item with a pre-acknowledged one. While the turn runs, a pending idle item is now left exactly as found, the page's stop handler returns on the keep-alive reason before clearing hooks or raising Response Complete, and session:working/session:idle carry keepAlive so the stuck-detection timer neither restarts nor re-arms.

The window that marks the turn closes on its own idle prompt or any other submit instead of a fixed three minutes, which a slow turn's idle prompt (sent a minute after the turn ends) could outlast. The service keeps the default and cap in memory, read through a strict reader so a mid-write read is retried rather than kept, and the cap is clamped before the strict settings save.

test/mocks/mock-session.ts

@@ -56,6 +56,9 @@ export class MockSession extends EventEmitter {
   }
   /** Mirrors the prompt-cache keep-warm surface on Session (prompt-cache-keepwarm.ts). */
   keepAliveTurnActive = false;
+  endKeepAliveTurn(): void {
+    this.keepAliveTurnActive = false;
+  }
   keepWarmEnabled: boolean | undefined = undefined;
   setKeepWarmEnabled(enabled: boolean | undefined): void {
     this.keepWarmEnabled = enabled;