fix(tracker): live sync label truncation and due_day fallback on partial update

- Shorten 'Live Sync' label to 'Live' for space-constrained layouts
- Add existing bill due_day fallback in validateBillData to prevent
  spurious required-field errors during partial PATCH updates

(batch 0.37.2)

client/pages/TrackerPage.jsx

@@ -813,7 +813,7 @@ export default function TrackerPage() {
                     <span className="absolute inline-flex h-full w-full animate-ping rounded-full bg-emerald-400 opacity-75" />
                     <span className="relative inline-flex h-1.5 w-1.5 rounded-full bg-emerald-500" />
                   </span>
-                  Live Sync
+                  Live
                 </span>
               </div>
               <p className="text-[1.75rem] font-bold tracking-tight font-mono leading-none text-foreground">

services/billsService.js

@@ -254,9 +254,13 @@ function validateBillData(data, existingBill = null) {
   }
   normalized.name = nameVal || null;
 
-  // due_day is required
+  // due_day is required; fall back to existing value on partial updates
   if (data.due_day === undefined || data.due_day === null) {
-    errors.push({ field: 'due_day', message: 'due_day is required' });
+    if (existingBill?.due_day != null) {
+      normalized.due_day = existingBill.due_day;
+    } else {
+      errors.push({ field: 'due_day', message: 'due_day is required' });
+    }
   } else {
     const dueResult = parseDueDay(data.due_day);
     if (dueResult.error) {