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.

src/web/server.ts

@@ -99,7 +99,7 @@ import { getLifecycleLog } from '../session-lifecycle-log.js';
 import {
   applyWorkspaceHooks,
   pruneAgentSessionPreambles,
-  readKeepWarmSettings,
+  readKeepWarmSettingsOrThrow,
   removeAgentSessionPreamble,
 } from '../hooks-config.js';
 import { PushSubscriptionStore } from '../push-store.js';
@@ -332,7 +332,7 @@ export class WebServer extends EventEmitter {
   private readonly keepWarmService = new PromptCacheKeepWarmService({
     getSession: (id) => this.sessions.get(id),
     sessionIds: () => this.sessions.keys(),
-    readSettings: readKeepWarmSettings,
+    readSettings: readKeepWarmSettingsOrThrow,
     isAutomationActive: (id) => {
       const session = this.sessions.get(id);
       if (!session) return true;