fix: implement timezone-aware datetime display and editing

All datetime values are stored in UTC but were displaying raw UTC times
to users, causing confusion (e.g., 10:00 Bucharest showing as 08:00).
This implements proper timezone conversion throughout the app using each
user's profile timezone setting.

Changes:
- Frontend: Replace local formatters with timezone-aware utilities
- Backend: Add timezone conversion to PUT /bookings endpoint
- FullCalendar: Configure to display events in user timezone
- Fix edit modal to preserve times when editing bookings

Co-Authored-By: Claude Sonnet 4.5 <noreply@anthropic.com>

frontend/src/views/AdminPending.vue

@@ -140,10 +140,14 @@
 </template>
 
 <script setup lang="ts">
-import { ref, onMounted } from 'vue'
+import { ref, computed, onMounted } from 'vue'
 import { adminBookingsApi, spacesApi, handleApiError } from '@/services/api'
+import { useAuthStore } from '@/stores/auth'
+import { formatDate as formatDateUtil, formatTime as formatTimeUtil } from '@/utils/datetime'
 import type { Booking, Space } from '@/types'
 
+const authStore = useAuthStore()
+const userTimezone = computed(() => authStore.user?.timezone || 'UTC')
 const bookings = ref<Booking[]>([])
 const spaces = ref<Space[]>([])
 const loading = ref(false)
@@ -179,24 +183,13 @@ const loadSpaces = async () => {
 }
 
 const formatDate = (datetime: string): string => {
-  const date = new Date(datetime)
-  return date.toLocaleDateString('en-GB', {
-    day: '2-digit',
-    month: 'short',
-    year: 'numeric'
-  })
+  return formatDateUtil(datetime, userTimezone.value)
 }
 
 const formatTime = (start: string, end: string): string => {
-  const startDate = new Date(start)
-  const endDate = new Date(end)
-  const formatTimeOnly = (date: Date) =>
-    date.toLocaleTimeString('en-GB', {
-      hour: '2-digit',
-      minute: '2-digit',
-      hour12: false
-    })
-  return `${formatTimeOnly(startDate)} - ${formatTimeOnly(endDate)}`
+  const startTime = formatTimeUtil(start, userTimezone.value)
+  const endTime = formatTimeUtil(end, userTimezone.value)
+  return `${startTime} - ${endTime}`
 }
 
 const formatType = (type: string): string => {