Refactor HAOS integration to use shared core library (Phase 2)

Wire the integration to delegate all HA-independent logic to
immich-watcher-core, eliminating ~2300 lines of duplicated code.

Changes:
- const.py: Import shared constants from core, keep HA-specific ones
- storage.py: Create HAStorageBackend adapter wrapping HA's Store,
  use core TelegramFileCache and NotificationQueue via adapter
- coordinator.py: Delegate to core ImmichClient for API calls,
  detect_album_changes() for change detection, and asset_utils
  for filtering/sorting/URL building. Keep HA-specific event firing.
- sensor.py: Replace ~1300 lines of Telegram code with 15-line
  delegation to core TelegramClient. Keep entity classes unchanged.
- __init__.py: Use factory functions for creating core instances
  with HA storage backends
- manifest.json: Add immich-watcher-core dependency

Integration line count: 3600 -> 1295 lines (-64%)
Zero behavior changes for end users.

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

custom_components/immich_album_watcher/manifest.json

@@ -7,6 +7,6 @@
     "documentation": "https://github.com/DolgolyovAlexei/haos-hacs-immich-album-watcher",
     "iot_class": "cloud_polling",
     "issue_tracker": "https://github.com/DolgolyovAlexei/haos-hacs-immich-album-watcher/issues",
-    "requirements": [],
+    "requirements": ["immich-watcher-core==0.1.0"],
     "version": "2.8.0"
 }