fix: harden booking and meeting flows

lib/calendar/timezone.ts

@@ -2,6 +2,15 @@ const BERLIN_TZ = "Europe/Berlin";
 
 export type CalendarDate = { year: number; month: number; day: number };
 
+/** Strict calendar input, interpreted in Berlin regardless of server TZ. */
+export function parseBerlinDate(value: string): Date | null {
+  if (!/^\d{4}-\d{2}-\d{2}$/.test(value)) return null;
+  const [year, month, day] = value.split("-").map(Number);
+  if (year < 1000 || month < 1 || month > 12 || day < 1 || day > 31) return null;
+  const date = berlinWallTimeToUTC({ year, month, day }, 0, 0);
+  return berlinDateKey(date) === value ? date : null;
+}
+
 export function berlinDateKey(date: Date): string {
   const { year, month, day } = berlinParts(date);
   return `${year}-${String(month).padStart(2, "0")}-${String(day).padStart(2, "0")}`;