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/api/client.ts

@@ -184,6 +184,7 @@ export const budgetApi = {
   setMembers: (tripId: number | string, id: number, userIds: number[]) => apiClient.put(`/trips/${tripId}/budget/${id}/members`, { user_ids: userIds }).then(r => r.data),
   togglePaid: (tripId: number | string, id: number, userId: number, paid: boolean) => apiClient.put(`/trips/${tripId}/budget/${id}/members/${userId}/paid`, { paid }).then(r => r.data),
   perPersonSummary: (tripId: number | string) => apiClient.get(`/trips/${tripId}/budget/summary/per-person`).then(r => r.data),
+  settlement: (tripId: number | string) => apiClient.get(`/trips/${tripId}/budget/settlement`).then(r => r.data),
 }
 
 export const filesApi = {