Derive slot validation from config instead of hardcoded values

- Created _get_valid_minute_boundaries() helper that derives valid minutes from SLOT_DURATION_MINUTES
- Replaced hardcoded (0, 15, 30, 45) with dynamic calculation
- Error message now includes valid minute values for better clarity

backend/routes/booking.py

@@ -46,6 +46,19 @@ def _to_appointment_response(
     )
 
 
+def _get_valid_minute_boundaries() -> tuple[int, ...]:
+    """Get valid minute boundaries based on SLOT_DURATION_MINUTES.
+    
+    Assumes SLOT_DURATION_MINUTES divides 60 evenly (e.g., 15 minutes = 0, 15, 30, 45).
+    """
+    boundaries: list[int] = []
+    minute = 0
+    while minute < 60:
+        boundaries.append(minute)
+        minute += SLOT_DURATION_MINUTES
+    return tuple(boundaries)
+
+
 def _get_bookable_date_range() -> tuple[date, date]:
     """Get the valid date range for booking (tomorrow to +30 days)."""
     today = date.today()
@@ -148,11 +161,12 @@ async def create_booking(
     slot_date = request.slot_start.date()
     _validate_booking_date(slot_date)
     
-    # Validate slot is on 15-minute boundary
+    # Validate slot is on the correct minute boundary (derived from SLOT_DURATION_MINUTES)
-    if request.slot_start.minute not in (0, 15, 30, 45):
+    valid_minutes = _get_valid_minute_boundaries()
+    if request.slot_start.minute not in valid_minutes:
         raise HTTPException(
             status_code=400,
-            detail="Slot start time must be on 15-minute boundary",
+            detail=f"Slot start time must be on {SLOT_DURATION_MINUTES}-minute boundary (valid minutes: {valid_minutes})",
         )
     if request.slot_start.second != 0 or request.slot_start.microsecond != 0:
         raise HTTPException(