Notifications card: show unread count bubble via the shared poll

pollNotifications now updates every .notif-badge (sidebar nav + homepage card)
from the same /api/notifications source, so the card bubble shows the unread
count and clears in lockstep with the sidebar. Add a badge to the card; scope
the collapsed-only badge positioning to the sidebar.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

manager/templates/home.html

@@ -75,6 +75,7 @@
   <a class="tile" href="/notifications">
     <span class="t-ico">🔔</span>
     <span class="t-title">Notifications</span>
+    <span class="notif-badge" style="display:none;"></span>
   </a>
   <a class="tile" href="/settings">
     <span class="t-ico">⚙️</span>