Calendar Integration

Lead asks to book -> agent checks availability -> booking card appears
  -> visitor chooses a slot -> event is created -> confirmation email is sent

When a visitor asks to book a call, collect their name, email,
timezone, and preferred duration if missing.

Use calendar_check_availability to find real open slots. If slots are
returned, show them with calendar_request_booking. Do not say there are
no available slots when availability returned slots.

After the visitor chooses a slot, use calendar_create_event to create
the event. calendar_create_event sends the attendee confirmation email,
so do not use notify_user as a calendar invite unless the visitor asks
for a separate follow-up notification.

In the final response, confirm the meeting time from display_time when
the tool returns it.