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  - Fallback to active WeekTemplates for unpublished dates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  - Delete unpublished slots or set to CLOSED if bookings exist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/server/src/time-slot/time-slot.controller.ts

@@ -20,6 +20,7 @@ import { SlotGeneratorService } from './slot-generator.service'
 import { QuerySlotsDto } from './dto/query-slots.dto'
 import { CreateManualSlotDto } from './dto/create-manual-slot.dto'
 import { UpdateWeekTemplateDto } from './dto/week-template.dto'
+import { PublishDaySlotsDto } from './dto/publish-day-slots.dto'
 
 // ---------------------------------------------------------------------------
 // Member endpoints
@@ -89,4 +90,17 @@ export class AdminTimeSlotController {
   generateSlots() {
     return this.slotGeneratorService.generateSlots()
   }
+
+  // Schedule preview & publish
+
+  @Get('schedule/preview')
+  getSchedulePreview(@Query('date') date: string) {
+    return this.timeSlotService.getSchedulePreview(date)
+  }
+
+  @Post('schedule/publish')
+  @HttpCode(HttpStatus.OK)
+  publishDaySlots(@Body() dto: PublishDaySlotsDto) {
+    return this.timeSlotService.publishDaySlots(dto)
+  }
 }