Add event type handling for duties in the system

- Introduced a new `event_type` column in the `duties` table to categorize duties as 'duty', 'unavailable', or 'vacation'.
- Updated the duty schedule import functionality to parse and store event types from the JSON input.
- Enhanced the API response to include event types for each duty, improving the calendar display logic.
- Modified the web application to visually differentiate between duty types in the calendar and duty list.
- Updated tests to cover new event type functionality and ensure correct parsing and storage of duties.
- Revised README documentation to reflect changes in duty event types and their representation in the system.

db/repository.py

@@ -102,9 +102,16 @@ def insert_duty(
     user_id: int,
     start_at: str,
     end_at: str,
+    event_type: str = "duty",
 ) -> Duty:
-    """Create a duty. start_at and end_at must be UTC, ISO 8601 with Z (e.g. 2025-01-15T09:00:00Z)."""
-    duty = Duty(user_id=user_id, start_at=start_at, end_at=end_at)
+    """Create a duty. start_at and end_at must be UTC, ISO 8601 with Z.
+    event_type: 'duty' | 'unavailable' | 'vacation'."""
+    duty = Duty(
+        user_id=user_id,
+        start_at=start_at,
+        end_at=end_at,
+        event_type=event_type,
+    )
     session.add(duty)
     session.commit()
     session.refresh(duty)