Channel features: subscribers, new-videos badges, activity-driven sync

- Store subscriber count from YouTube statistics and show it on channel page
- Sync 50 videos per channel with playlistItems pagination support
- Show per-channel and per-category new-videos counters (2-day window)
- Replace hourly videos sync with activity trigger (2h idle) and
  incremental backfill (hard cap 200 per channel)
- Clicking the sidebar new-videos count filters the category feed to
  recent videos only (new_only)
- Update agent-team docs: deploy after green checks

backend/app/api/categories.py

@@ -1,14 +1,19 @@
+from datetime import datetime, timedelta, timezone
+
 from fastapi import APIRouter, Depends, HTTPException
 from pydantic import BaseModel, Field
 from sqlalchemy import func
 from sqlalchemy.exc import IntegrityError
 from sqlalchemy.orm import Session
 
+from app.config import settings
 from app.core.auth_dependency import require_session
 from app.core.slugify import unique_slugify
 from app.db import get_db
 from app.models.category import Category
+from app.models.channel import Channel
 from app.models.channel_category import channel_categories
+from app.models.video import Video
 
 router = APIRouter(dependencies=[Depends(require_session)])
 
@@ -40,13 +45,15 @@ def _name_taken(db: Session, name: str, exclude_id: int | None = None) -> bool:
     return any(row[0].casefold() == target for row in query.all())
 
 
-def _serialize(db: Session, category: Category, counts: dict[int, int]) -> dict:
+def _serialize(db: Session, category: Category, counts: dict[int, int], new_videos: dict[int, int] | None = None) -> dict:
+    new_videos = new_videos or {}
     return {
         "id": category.id,
         "name": category.name,
         "slug": category.slug,
         "sort_order": category.sort_order,
         "channel_count": counts.get(category.id, 0),
+        "new_videos_count": new_videos.get(category.id, 0),
     }
 
 
@@ -59,7 +66,17 @@ def list_categories(db: Session = Depends(get_db)) -> list[dict]:
         .all()
     )
     counts = dict(count_rows)
-    return [_serialize(db, c, counts) for c in categories]
+    since = datetime.now(timezone.utc) - timedelta(days=settings.new_videos_window_days)
+    new_videos_rows = (
+        db.query(channel_categories.c.category_id, func.count(Video.id))
+        .join(Channel, Channel.id == channel_categories.c.channel_id)
+        .join(Video, Video.channel_id == Channel.id)
+        .filter(Channel.subscribed.is_(True), Video.published_at >= since)
+        .group_by(channel_categories.c.category_id)
+        .all()
+    )
+    new_videos = dict(new_videos_rows)
+    return [_serialize(db, c, counts, new_videos) for c in categories]
 
 
 @router.post("/categories", status_code=201)