Sync a trip itinerary to Google Calendar via the Calendar API

Steps

1. Authenticate with the Google Calendar API using OAuth 2.0 with the calendar.events scope; request offline access to obtain a refresh token for background syncing.
2. For each confirmed itinerary segment, create a Calendar event by calling POST /calendars/{calendarId}/events with summary (e.g., 'Flight UA 123: JFK → LAX'), start and end datetimes with timezone, location, and a description containing the confirmation number and key details.
3. Use the event's extendedProperties.private object to store your internal booking ID and segment type so you can identify and update events later.
4. For hotel segments, set the event's start to check-in date (at standard check-in time) and end to check-out date; set location to the hotel address for map integration.
5. On booking update or cancellation, retrieve the corresponding Calendar event by querying extendedProperties and call PATCH or DELETE accordingly.
6. Provide a user-facing toggle to enable/disable calendar sync and respect revocation of OAuth consent by catching 401 errors and prompting re-authorization.