feat: expense settlement — track who paid, show who owes whom — closes #41

- Click member avatars on budget items to mark who paid (green = paid)
- Multiple green chips = those people split the payment equally
- Settlement dropdown in the total budget card shows optimized payment
  flows (who owes whom how much) and net balances per person
- Info tooltip explains how the feature works
- New server endpoint GET /budget/settlement calculates net balances
  and minimized payment flows using a greedy algorithm
- Merged category legend: amount + percentage in one row
- i18n keys added for DE and EN

client/src/i18n/translations/de.ts

@@ -800,6 +800,9 @@ const de: Record<string, string | { name: string; category: string }[]> = {
   'budget.paid': 'Bezahlt',
   'budget.open': 'Offen',
   'budget.noMembers': 'Keine Teilnehmer zugewiesen',
+  'budget.settlement': 'Ausgleich',
+  'budget.settlementInfo': 'Klicke auf ein Mitglied-Bild bei einem Eintrag, um es grün zu markieren — das bedeutet, diese Person hat bezahlt. Der Ausgleich zeigt dann, wer wem wie viel schuldet.',
+  'budget.netBalances': 'Netto-Salden',
 
   // Files
   'files.title': 'Dateien',

client/src/i18n/translations/en.ts

@@ -800,6 +800,9 @@ const en: Record<string, string | { name: string; category: string }[]> = {
   'budget.paid': 'Paid',
   'budget.open': 'Open',
   'budget.noMembers': 'No members assigned',
+  'budget.settlement': 'Settlement',
+  'budget.settlementInfo': 'Click a member avatar on a budget item to mark them green — this means they paid. The settlement then shows who owes whom and how much.',
+  'budget.netBalances': 'Net Balances',
 
   // Files
   'files.title': 'Files',