feat(feed): /api/facets endpoint for contextual tag counts

Add a facets endpoint that returns per-tag channel counts for the current filter
context (scope, channel, date, content type, search, watch state, and the other
category's tags). Each category is counted with its own selections ignored —
standard drill-down faceting — by a new exclude_tag_category param threaded into
_filtered_query, so selecting one topic doesn't zero out the other topics. Count
is distinct channels with a matching video, keeping the channel-count chip
semantics. Reuses the feed's filter query so both stay in lockstep.

backend/app/routes/feed.py

@@ -67,6 +67,7 @@ def _filtered_query(
     include_live: bool,
     show: str,
     scope: str = "my",
+    exclude_tag_category: str | None = None,
 ) -> tuple[Select, object]:
     """Build the feed query (joins + all WHERE filters), shared by /feed and /feed/count.
     Returns the column-bearing select plus the watch-status expression for sorting.
@@ -153,6 +154,11 @@ def _filtered_query(
         by_category: dict[str, list[int]] = {}
         for tag_id, category in cat_rows:
             by_category.setdefault(category, []).append(tag_id)
+        # Facet counting drops the category being counted so its own chips don't zero each
+        # other out (standard drill-down faceting: a category's count ignores its own
+        # selections but still honours the other categories' filters).
+        if exclude_tag_category:
+            by_category.pop(exclude_tag_category, None)
         visible = or_(ChannelTag.user_id.is_(None), ChannelTag.user_id == user.id)
         for category, ids in by_category.items():
             if category == "topic" and tag_mode == "and" and len(ids) > 1:
@@ -294,6 +300,41 @@ def get_feed_count(
     return {"count": total or 0}
 
 
+@router.get("/facets")
+def get_facets(
+    params: dict = Depends(_feed_params),
+    user: User = Depends(current_user),
+    db: Session = Depends(get_db),
+) -> dict:
+    """Per-tag channel counts for the *current* filter context, so the sidebar can show
+    live counts and drop chips that no longer match anything. Each category is counted with
+    every other filter applied (scope, channel, date, content type, search, watch state,
+    and the other category's tags) but its own selections ignored — standard drill-down
+    faceting, so selecting one topic doesn't zero out the rest of the topics.
+
+    The count is the number of distinct channels that have at least one video in the current
+    view, matching the existing channel-count chip semantics. JSON object keys are strings
+    (tag ids)."""
+    visible = or_(ChannelTag.user_id.is_(None), ChannelTag.user_id == user.id)
+    counts: dict[int, int] = {}
+    for category in ("language", "topic"):
+        base, _status = _filtered_query(
+            db, user, **{**params, "exclude_tag_category": category}
+        )
+        channels = base.with_only_columns(Video.channel_id).distinct().subquery()
+        rows = db.execute(
+            select(ChannelTag.tag_id, func.count(func.distinct(ChannelTag.channel_id)))
+            .select_from(channels)
+            .join(ChannelTag, ChannelTag.channel_id == channels.c.channel_id)
+            .join(Tag, and_(Tag.id == ChannelTag.tag_id, Tag.category == category))
+            .where(visible)
+            .group_by(ChannelTag.tag_id)
+        ).all()
+        for tag_id, count in rows:
+            counts[tag_id] = count
+    return {"counts": counts}
+
+
 @router.post("/videos/{video_id}/state")
 def set_video_state(
     video_id: str,