feat(admin): implement full day-by-day schedule editor with live preview

## Features

### Admin Schedule Page (`packages/app/src/pages/admin/schedule.vue`)
- Interactive date-based slot editor for managing daily schedules
- Real-time slot editing: start/end times, capacity adjustments
- Slot deletion with conflict warnings when bookings exist
- Add new slots with modal dialog
- Live booking status display (booked count, people names)
- Publish/Save changes with sync feedback
- Revert unsaved changes with confirmation
- Skeleton loading states and empty state handling
- Responsive design with optimized mobile UX

### Backend Enhancements
- **New DTO** (`PublishDaySlotsDto`): Structured slot publishing with validation
  - Date string validation
  - Slot array with existing slot IDs for updates
  - Time and capacity validation per slot

- **Schedule Preview API** (`getSchedulePreview`):
  - Check for existing published slots
  - Fallback to active WeekTemplates for unpublished dates
  - Unified response format with isPublished flag

- **Publish Slots API** (`publishDaySlots`):
  - Atomic transaction for consistency
  - Update existing slots with new times/capacity
  - Create new slots from template data
  - Delete unpublished slots or set to CLOSED if bookings exist
  - Prevent capacity reduction below existing bookings
  - Returns all published slots for feedback

### State Management
- Enhanced admin store with schedule state
- Support for pending/unsaved slot changes
- Optimistic UI updates with server sync

### Documentation
- Comprehensive scheduling system architecture docs
- Quick reference for admin workflows
- Flow diagrams and state transitions
- Implementation guide for future maintenance

## Breaking Changes
None

## Testing Recommendations
- Create slots for future dates via schedule editor
- Verify booking prevention for locked/full slots
- Test capacity adjustments with existing bookings
- Confirm template-based schedule generation
- Verify transaction rollback on publish failures

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

pnpm-lock.yaml

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+      '@types/multer':
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+        version: 1.4.13
       '@types/passport-jwt':
         specifier: ^4.0.1
         version: 4.0.1
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+  '@types/multer@1.4.13':
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+
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@@ -7168,6 +7174,10 @@ snapshots:
 
   '@types/ms@2.1.0': {}
 
+  '@types/multer@1.4.13':
+    dependencies:
+      '@types/express': 4.17.25
+
   '@types/node@20.19.37':
     dependencies:
       undici-types: 6.21.0