feat: home page logout stays + wider PC layout

- logout() on home/root page: Auth.reset() only (clear state, refresh
  top bar), no redirect to login; other pages still go to login
- home page container: width:min(50vw+300px, 1440px, 96vw) replaces
  fixed max-width:800px - PC wide screens use at least half viewport,
  mobile near full width

public/js/app.js

@@ -83,7 +83,16 @@ const App = {
   },
 
   afterLogin() { location.hash = '#/dashboard'; },
-  logout() { Auth.logout(); },
+  logout() {
+    // 首页/根路径为公开页: 退出仅清除登录态, 停留当前页刷新顶栏; 其他页面才回登录页
+    const page = (location.hash || '#/home').replace('#/', '').split('/')[0];
+    if (page === 'home' || page === '') {
+      Auth.reset();
+      this.updateTopAuth();
+    } else {
+      Auth.logout();
+    }
+  },
   closeModal() { document.getElementById('modal-overlay').classList.add('hidden'); },
   navigate(page, param) { location.hash = `#/${page}` + (param ? `/${param}` : ''); },