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/components/app-sidebar.tsx

@@ -47,6 +47,7 @@ import { ThemePreferenceMenu } from "@/components/theme-preference-menu";
 import { UserAvatar } from "@/components/user-avatar";
 import type { BeamAvatar } from "@/lib/beam-avatar";
 import { groupSessionsByRecency } from "@/lib/session-groups";
+import { markNewChatClick } from "@/lib/new-chat-timing";
 
 export type SidebarAccount = {
   name: string;
@@ -185,6 +186,12 @@ export function AppSidebar({
     closeDrawer();
   }
 
+  /** Off `/`: the same drawer close, plus the click mark for new-chat timing (BUG-1104). */
+  function handleNewChatLink() {
+    markNewChatClick();
+    closeDrawer();
+  }
+
   /* Real links. Leaving `/` used to be a full document load: the whole React
      tree, the session list and the account went with it, so coming back re-ran
      the entire bootstrap from zero. `/login` keeps the hard exit —
@@ -278,7 +285,7 @@ export function AppSidebar({
                 {showExpandedContent ? <span>{creatingSession ? "正在创建" : "新建对话"}</span> : null}
               </SidebarMenuButton>
             ) : (
-              <SidebarMenuLink className="new-chat" tooltip="新对话" href={newChatHref()} onClick={closeDrawer}>
+              <SidebarMenuLink className="new-chat" tooltip="新对话" href={newChatHref()} onClick={handleNewChatLink}>
                 <SquarePen size={18} strokeWidth={1.75} aria-hidden="true" />
                 {showExpandedContent ? <span>新建对话</span> : null}
               </SidebarMenuLink>