fix(telegram): unify send routine across notifications and commands

- Route cache_key values that look like asset UUIDs through asset_cache
  in TelegramClient._get_cache_and_key. Single-asset sends previously
  stored file_ids in url_cache while the media-group path stored them
  in asset_cache, so repeat sends never hit.
- Extract build_asset_media_urls so the notification dispatcher
  (asset_to_media) and the bot command handlers (common._format_assets)
  share one rule for /video/playback vs thumbnail URLs.
- Add services/telegram_send.py as the single factory for constructing
  a TelegramClient. It always wires the shared aiohttp session and both
  file caches, so commands now reuse file_ids populated by notification
  dispatches (and vice versa) instead of re-uploading the same bytes.
- send_reply / send_media_group in commands/handler.py now delegate to
  the factory rather than constructing their own uncached clients.

packages/server/src/notify_bridge_server/commands/immich/common.py

@@ -7,7 +7,10 @@ import logging
 from typing import Any
 
 from notify_bridge_core.notifications.telegram.media import build_telegram_asset_entry
-from notify_bridge_core.providers.immich.asset_utils import get_public_url
+from notify_bridge_core.providers.immich.asset_utils import (
+    build_asset_media_urls,
+    get_public_url,
+)
 
 from ..handler import _render_cmd_template
 
@@ -127,21 +130,19 @@ def _format_assets(
     })
 
     if response_mode == "media":
-        # Reuse the same entry-building helper as the notification dispatcher
-        # so videos keep their "video" type and point at /video/playback —
-        # typing them as "photo" made Telegram render the still poster
-        # thumbnail in media groups instead of the real clip.
+        # Reuse the same URL rule (build_asset_media_urls) and entry builder
+        # (build_telegram_asset_entry) as the notification dispatcher so both
+        # paths agree on video → /video/playback and photo → thumbnail. When
+        # these diverged, Telegram rendered a still JPEG for each video in
+        # the media group instead of the real clip.
         media_items: list[dict[str, Any]] = []
         for asset in assets:
             asset_id = asset.get("id", "")
-            is_video = (asset.get("type") or "").upper() == "VIDEO"
-            if is_video:
-                url = f"{client.url}/api/assets/{asset_id}/video/playback"
-            else:
-                url = f"{client.url}/api/assets/{asset_id}/thumbnail?size=preview"
+            asset_type = (asset.get("type") or "").upper()
+            preview_url, _ = build_asset_media_urls(client.url, asset_id, asset_type)
             entry = build_telegram_asset_entry(
-                url=url,
-                media_type="video" if is_video else "image",
+                url=preview_url,
+                media_type="video" if asset_type == "VIDEO" else "image",
                 api_key=client.api_key,
                 internal_url=client.url,
                 cache_key=asset_id,