Refactor duty authentication and event type handling

- Introduced a new function `get_authenticated_username` to centralize Mini App authentication logic, improving code readability and maintainability.
- Updated the duty fetching logic to map unknown event types to "duty" for consistent API responses.
- Enhanced the `get_duties` function to include duties starting on the last day of the specified date range.
- Improved session management in the database layer to ensure rollback on exceptions.
- Added tests to validate the new authentication flow and event type handling.

db/schemas.py

@@ -40,7 +40,10 @@ class DutyInDb(DutyBase):
 
 
 class DutyWithUser(DutyInDb):
-    """Duty with full_name and event_type for calendar display."""
+    """Duty with full_name and event_type for calendar display.
+
+    event_type: only these values are returned; unknown DB values are mapped to "duty" in the API.
+    """
 
     full_name: str
     event_type: Literal["duty", "unavailable", "vacation"] = "duty"