Integrate LiveKit SFU and harden booking workflow

lib/format.ts

@@ -1,14 +1,16 @@
+import { formatBerlinDate, formatBerlinTime } from "@/lib/calendar/timezone";
+
 /** Day + short month, e.g. { day: "15", month: "SEP" } — for the date badge on event cards. */
 export function formatEventDateParts(iso: string) {
   const date = new Date(iso);
   return {
-    day: date.toLocaleDateString("de-DE", { day: "2-digit" }),
-    month: date.toLocaleDateString("de-DE", { month: "short" }).toUpperCase().replace(".", ""),
+    day: formatBerlinDate(date, { day: "2-digit" }),
+    month: formatBerlinDate(date, { month: "short" }).toUpperCase().replace(".", ""),
   };
 }
 
 export function formatFullDate(iso: string) {
-  return new Date(iso).toLocaleDateString("de-DE", {
+  return formatBerlinDate(new Date(iso), {
     weekday: "long",
     day: "2-digit",
     month: "long",
@@ -17,7 +19,7 @@ export function formatFullDate(iso: string) {
 }
 
 export function formatTime(iso: string) {
-  return new Date(iso).toLocaleTimeString("de-DE", { hour: "2-digit", minute: "2-digit" });
+  return formatBerlinTime(new Date(iso), { hour: "2-digit", minute: "2-digit" });
 }
 
 export function formatTimeRange(start?: string | null, end?: string | null) {