Add complete settlement system with visual distinction

- Add settlement category with handshake emoji (🤝)
- Create settlement page for recording debt payments with user → user flow
- Implement settlement detection and visual styling across all views
- Add conditional "Settle Debts" button (hidden when balance is 0)
- Style settlement payments distinctly in recent activity with large profile pictures
- Add settlement flow styling in payments overview with green theme
- Update backend validation and Mongoose schema for settlement category
- Fix settlement receiver detection with proper user flow logic

🤝 Generated with [Claude Code](https://claude.ai/code)

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

src/routes/api/cospend/payments/+server.ts

@@ -52,7 +52,7 @@ export const POST: RequestHandler = async ({ request, locals }) => {
     throw error(400, 'Invalid split method');
   }
 
-  if (category && !['groceries', 'shopping', 'travel', 'restaurant', 'utilities', 'fun'].includes(category)) {
+  if (category && !['groceries', 'shopping', 'travel', 'restaurant', 'utilities', 'fun', 'settlement'].includes(category)) {
     throw error(400, 'Invalid category');
   }