Resolve "Consultations and calendar integration - add consultations to calendar (two way sync) for professor"
requested to merge 27-consultations-and-calendar-integration-add-consultations-to-calendar-two-way-sync-for-professor into dev
- added consultations and calendar integration updates
- implemented reverse sync behavior
- updated Google and Outlook calendar related logic
- adjusted consultation status synchronization
- included latest fixes for scheduler and consultation flow