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  - Fallback to active WeekTemplates for unpublished dates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  - Delete unpublished slots or set to CLOSED if bookings exist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>

packages/app/src/stores/admin.ts

@@ -13,6 +13,8 @@ import type {
   TimeSlot,
   CreateManualSlotDto,
   PaginatedData,
+  ScheduleSlotPreview,
+  PublishDaySlotsDto,
 } from '@mp-pilates/shared'
 
 export interface AdminStats {
@@ -42,7 +44,7 @@ export const useAdminStore = defineStore('admin', () => {
   }
 
   async function saveWeekTemplates(templates: WeekTemplateInput[]): Promise<WeekTemplate[]> {
-    const data = await put<WeekTemplate[]>('/admin/week-template', templates)
+    const data = await put<WeekTemplate[]>('/admin/week-template', { templates })
     weekTemplates.value = data
     return data
   }
@@ -132,6 +134,26 @@ export const useAdminStore = defineStore('admin', () => {
     return post<{ count: number }>('/admin/generate-slots', { startDate, endDate })
   }
 
+  // ── Schedule management ─────────────────────────────────────────
+  const schedulePreview = ref<ScheduleSlotPreview[]>([])
+  const scheduleLoading = ref(false)
+
+  async function fetchSchedulePreview(date: string): Promise<ScheduleSlotPreview[]> {
+    scheduleLoading.value = true
+    try {
+      const data = await get<ScheduleSlotPreview[]>('/admin/schedule/preview', { date })
+      schedulePreview.value = data
+      return data
+    } finally {
+      scheduleLoading.value = false
+    }
+  }
+
+  async function publishDaySlots(dto: PublishDaySlotsDto): Promise<void> {
+    await post('/admin/schedule/publish', dto as unknown as Record<string, unknown>)
+    await fetchSchedulePreview(dto.date)
+  }
+
   // ── Dashboard stats ──────────────────────────────────────────────
   async function fetchDashboardStats(): Promise<AdminStats> {
     return get<AdminStats>('/admin/stats')
@@ -142,6 +164,8 @@ export const useAdminStore = defineStore('admin', () => {
     weekTemplates,
     cardTypes,
     studioConfig,
+    schedulePreview,
+    scheduleLoading,
     // Week templates
     fetchWeekTemplates,
     saveWeekTemplates,
@@ -164,6 +188,9 @@ export const useAdminStore = defineStore('admin', () => {
     createManualSlot,
     closeSlot,
     generateSlots,
+    // Schedule
+    fetchSchedulePreview,
+    publishDaySlots,
     // Stats
     fetchDashboardStats,
   }