Derive client domain types from the shared schema contracts

Add entity/response Zod schemas to @trek/shared (place, trip, assignment, day, budget, packing, reservation), each matched against the producing server service, and re-export them from client types.ts instead of the hand-written duplicates that had drifted (name/title, amount/total_price, owner_id/user_id, cover_url/cover_image, ...). Updates the call sites and test fixtures the corrected types surfaced; type-only, no runtime behaviour change.

client/src/components/Vacay/VacayCalendar.tsx

@@ -36,7 +36,7 @@ export default function VacayCalendar() {
   }, [selectedYear])
 
   const companyHolidaySet = useMemo(() => {
-    const s = new Set()
+    const s = new Set<string>()
     companyHolidays.forEach(h => s.add(h.date))
     return s
   }, [companyHolidays])