Integrate LiveKit SFU and harden booking workflow

lib/meeting/reminders.ts

@@ -2,6 +2,7 @@ import { getPayload } from "payload";
 import config from "@payload-config";
 import { combineDateAndTime } from "./status";
 import { sendReminderEmail } from "@/lib/email/sendReminderEmail";
+import { formatBerlinDate, formatBerlinTime } from "@/lib/calendar/timezone";
 
 const REMINDER_TOLERANCE_MS = 10 * 60 * 1000; // cron may run every few minutes
 
@@ -10,11 +11,11 @@ function isDue(reminderAt: number, now: number): boolean {
 }
 
 function formatDate(date: Date): string {
-  return date.toLocaleDateString("de-DE", { day: "2-digit", month: "long", year: "numeric" });
+  return formatBerlinDate(date, { day: "2-digit", month: "long", year: "numeric" });
 }
 
 function formatTime(date: Date): string {
-  return date.toLocaleTimeString("de-DE", { hour: "2-digit", minute: "2-digit" });
+  return formatBerlinTime(date, { hour: "2-digit", minute: "2-digit" });
 }
 
 /**