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/components/BookingForm.vue

@@ -319,6 +319,7 @@
 import { ref, computed, onMounted, watch } from 'vue'
 import { bookingsApi, bookingTemplatesApi, spacesApi, attachmentsApi, handleApiError } from '@/services/api'
 import { useAuthStore } from '@/stores/auth'
+import { formatDate as formatDateUtil } from '@/utils/datetime'
 import type {
   Space,
   BookingCreate,
@@ -328,6 +329,7 @@ import type {
 } from '@/types'
 
 const authStore = useAuthStore()
+const userTimezone = computed(() => authStore.user?.timezone || 'UTC')
 
 interface Props {
   spaceId?: number
@@ -396,8 +398,6 @@ const weekDays = ['Mon', 'Tue', 'Wed', 'Thu', 'Fri', 'Sat', 'Sun']
 // Computed values
 const activeSpaces = computed(() => spaces.value.filter((s) => s.is_active))
 
-const userTimezone = computed(() => authStore.user?.timezone || 'UTC')
-
 const selectedSpaceName = computed(() => {
   if (!props.spaceId) return ''
   const space = spaces.value.find((s) => s.id === props.spaceId)
@@ -454,7 +454,7 @@ const firstOccurrences = computed(() => {
   while (current <= end && dates.length < 5) {
     const dayIndex = current.getDay() === 0 ? 6 : current.getDay() - 1
     if (selectedDays.value.includes(dayIndex)) {
-      dates.push(current.toLocaleDateString('en-GB'))
+      dates.push(formatDateUtil(current.toISOString(), userTimezone.value))
     }
     current.setDate(current.getDate() + 1)
   }
@@ -853,7 +853,7 @@ const showRecurringResult = (result: RecurringBookingResult) => {
   if (result.total_skipped > 0) {
     message += `\n\nSkipped ${result.total_skipped} dates due to conflicts:`
     result.skipped_dates.slice(0, 5).forEach((skip) => {
-      const formattedDate = new Date(skip.date).toLocaleDateString('en-GB')
+      const formattedDate = formatDateUtil(skip.date, userTimezone.value)
       message += `\n- ${formattedDate}: ${skip.reason}`
     })
     if (result.total_skipped > 5) {