Add widget API endpoints for backstage dashboard integration

New GET /api/widget/recent — returns recent unwatched videos from followed
channels (title, channel, thumbnail, published_at, duration, direct URL).
New GET /api/widget/stats — unwatched count, new this week, channel count.

Both endpoints auth via X-Widget-Key header (WIDGET_API_KEY env var) so
external services can call without JWT token lifecycle management.
Targets the first admin user's data.

Also: pass WIDGET_API_KEY through docker-compose environment.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

backend/main.py

@@ -6,7 +6,7 @@ from fastapi.staticfiles import StaticFiles
 from .config import settings
 from .database import init_db, SessionLocal
 from .services import ytdlp as ytdlp_service
-from .routers import auth, channels, videos, search, downloads, discovery, settings as settings_router, stats as stats_router, export as export_router, collections as collections_router, admin as admin_router, playlists as playlists_router
+from .routers import auth, channels, videos, search, downloads, discovery, settings as settings_router, stats as stats_router, export as export_router, collections as collections_router, admin as admin_router, playlists as playlists_router, widget as widget_router
 
 app = FastAPI(title="YouTube Hub", version="0.1.0")
 
@@ -30,6 +30,7 @@ app.include_router(export_router.router, prefix="/api/export", tags=["export"])
 app.include_router(collections_router.router, prefix="/api/collections", tags=["collections"])
 app.include_router(admin_router.router, prefix="/api/admin", tags=["admin"])
 app.include_router(playlists_router.router, prefix="/api/playlists", tags=["playlists"])
+app.include_router(widget_router.router, prefix="/api/widget", tags=["widget"])
 
 
 os.makedirs(settings.download_path, exist_ok=True)