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/utils/datetime.ts

@@ -113,5 +113,5 @@ export const isoToLocalDateTime = (isoDateTime: string, timezone: string = 'UTC'
   const minute = date.toLocaleString('en-US', { timeZone: timezone, minute: '2-digit' })
 
   // Format as YYYY-MM-DDTHH:mm for datetime-local input
-  return `${year}-${month}-${day}T${hour.padStart(2, '0')}:${minute}`
+  return `${year}-${month}-${day}T${hour.padStart(2, '0')}:${minute.padStart(2, '0')}`
 }