feat(player): a video's related videos, on demand beside it

The player shows what YouTube lists beside the video, without what the
user has watched or hidden. Wide, a Related tab beside the description;
stacked, a button beside the info opens them in a drawer. A row plays in
the same player (Back returns) and the list stays the opened video's.
A switch picks on-topic or Hungarian-trending lists, kept on the account.

Each related row says whether the user follows its channel; the row is
the video card's narrow form with its whole menu. VideoMenu moves to
features/video, where the player can reach it.

backend/app/catalog/queries.py

@@ -158,6 +158,19 @@ def blocked_ids(db: Session, user: User) -> set[str]:
     )
 
 
+def followed_among(db: Session, user: User, channel_ids: set[str]) -> set[str]:
+    """Which of these channels the user subscribes to."""
+    if not channel_ids:
+        return set()
+    return set(
+        db.scalars(
+            select(Subscription.channel_id).where(
+                owned_by(Subscription.user_id, user), Subscription.channel_id.in_(channel_ids)
+            )
+        )
+    )
+
+
 def blocked_channels(db: Session, user: User, lang: str) -> list[Channel]:
     return list(
         db.execute(

backend/app/routes/search.py

@@ -284,8 +284,11 @@ def related_videos(
     # (a cursor) is the same list.
     if cursor is None:
         quota.log_action(user.id, quota.QuotaAction.VIDEOS_RELATED)
+    rows = reader_queries.feed_rows_by_ids(db, user, collected)
+    # A related list mixes channels the user follows with ones they never met: each row says which.
+    followed = queries.followed_among(db, user, {r["channel_id"] for r in rows})
     return {
-        "items": reader_queries.feed_rows_by_ids(db, user, collected),
+        "items": [{**r, "followed": r["channel_id"] in followed} for r in rows],
         "next_cursor": next_cursor,
         "has_more": bool(next_cursor),
     }