feat: Add /sync-bank endpoint to trigger bank sync and inference from web UI

Adds a new GET /sync-bank route that runs sync_to_sheets (2026) + infer_payments + flush_cache,
capturing all output and displaying it on a styled results page. Adds "Tools: [Sync Bank Data]"
nav link to all templates.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

templates/fees-juniors.html

@@ -192,6 +192,10 @@
             <a href="/reconcile-juniors">[Junior Payment Reconciliation]</a>
             <a href="/payments">[Payments Ledger]</a>
         </div>
+        <div class="nav-archived">
+            <span style="color: #666; margin-right: 5px;">Tools:</span>
+            <a href="/sync-bank">[Sync Bank Data]</a>
+        </div>
     </div>
 
     <h1>FUJ Junior Fees Dashboard</h1>