fix(home): prefetch the warm snapshot from secondary pages so the first 新建对话 skips the loading ring (BUG-1104)

Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01N4f2nya58RoRu4yEmJgRGE

frontend/src/app/(app)/page.tsx

@@ -14,7 +14,6 @@ import { HomeBootstrapError } from "@/components/home-bootstrap-error";
 import { HomeOnboardingShell } from "@/components/home-onboarding-shell";
 import { BirthSkyReveal } from "@/components/birth-sky/birth-sky-reveal";
 import {
-  entrySummaryFromResponse,
   rectificationEntryLabels,
   resolveRectificationEntryAction,
 } from "@/lib/rectification-entry";
@@ -159,12 +158,14 @@ import {
   discardLegacyCloudMirrorKeys,
   fetchCloudChartLibrary,
   fetchCloudSynastryHistory,
+  fetchRectificationEntrySummary,
   payloadCode,
   payloadMessage,
   waitForUndoWindow,
 } from "@/lib/home-cloud-sync";
 import { runHomeBootstrap, runHomeWarmRefresh } from "@/lib/home-bootstrap-run";
 import { writeHomeWarmSnapshot } from "@/lib/home-warm-snapshot";
+import { markHomeReadyAfterNewChat } from "@/lib/new-chat-timing";
 import {
   homeWarmStartInput,
   mountedHomeWarmStart,
@@ -507,10 +508,8 @@ export default function Home() {
     if (bootstrapPhase === "account" || !accountId || !sessionListSettled) return;
     void (async () => {
       try {
-        const response = await fetch("/api/rectification/cases/entry-summary", { cache: "no-store" });
-        if (!response.ok) return;
-        const payload = await response.json().catch(() => null);
-        setRectificationEntrySummary(entrySummaryFromResponse(payload));
+        const summary = await fetchRectificationEntrySummary();
+        if (summary) setRectificationEntrySummary(summary);
       } catch {
         // The CTA falls back to the server-agnostic default labels.
       } finally {
@@ -523,6 +522,7 @@ export default function Home() {
   // incomplete one (no catalog, summary not settled, error) is never written.
   useEffect(() => {
     if (!hydrated || uiPreview.current || accountError || !accountId || !modelCatalog || !rectificationEntrySummarySettled) return;
+    markHomeReadyAfterNewChat();
     writeHomeWarmSnapshot({
       accountId,
       modelCatalog,