feat(train-scheduling): implement day-level booking pool

- Added `unplaced` method in `BookingNotifierService` to log warnings for bookings that cannot be placed on any train.
- Introduced `getAvailableDays` method in `TrainSchedulingService` to retrieve distinct days with open departures for a given route.
- Created `AvailableDaysQueryDto` for querying available days based on origin and destination yards.
- Updated `TrainSchedulingController` to expose an endpoint for available days.
- Modified frontend components to support day-level booking, allowing customers to select only a day without pinning to a specific train.
- Removed references to train schedules in booking forms and review steps, emphasizing day selection.
- Added a database migration to create an index for efficient querying of bookings by route and day.

apps/edr-freight-web/backoffice/src/pages/bookings/NewBookingPage.tsx

@@ -302,8 +302,9 @@ export default function NewBookingPage() {
   const allLinesValid = lines.length > 0 && lines.every(lineValid);
   const sameYard = Boolean(originYardId && originYardId === destinationYardId);
 
-  const scheduleSatisfied =
-    hasBookableSchedules ? Boolean(trainScheduleId) : Boolean(scheduledDate);
+  // Day-level pool: a shipment DAY is enough to proceed. Pinning a specific train
+  // (trainScheduleId) is an optional staff override — the batch engine otherwise
+  // assigns the train. A selected schedule implies its day, so either satisfies.
   const departureSatisfied = Boolean(selectedSchedule) || Boolean(scheduledDate);
 
   const canSubmit =
@@ -311,7 +312,6 @@ export default function NewBookingPage() {
     Boolean(destinationYardId) &&
     !sameYard &&
     Boolean(tradeDirection) &&
-    scheduleSatisfied &&
     Boolean(serviceTypeId) &&
     departureSatisfied &&
     (isGovernment ? governmentInstitution.trim().length >= 2 : Boolean(companyId)) &&
@@ -473,25 +473,25 @@ export default function NewBookingPage() {
                 </Group>
                 {hasBookableSchedules ? (
                   <Select
-                    label="Train schedule"
+                    label="Train schedule (optional)"
                     placeholder={
                       originYardId && destinationYardId
-                        ? "Select an open schedule on this route"
+                        ? "Leave blank to let the batch engine assign a train"
                         : "Pick origin & destination first"
                     }
                     data={scheduleOptions}
                     value={trainScheduleId}
                     onChange={setTrainScheduleId}
                     searchable
-                    required
+                    clearable
                     disabled={!originYardId || !destinationYardId || schedulesLoading}
                     nothingFoundMessage="No open schedules on this route"
-                    description="The booking will be batched against this schedule once its contract is signed."
+                    description="Optional: pin to a specific train. Otherwise the booking joins the day pool and the engine assigns a train by priority."
                   />
                 ) : originYardId && destinationYardId ? (
                   <Text size="sm" c="dimmed">
-                    No open train schedule on this route — set a preferred departure below. Staff can
-                    link a schedule later.
+                    No open train schedule on this route — set a preferred departure below. The batch
+                    engine assigns a train on that day, or staff can pin one later.
                   </Text>
                 ) : null}
                 <Group grow align="flex-end">