perf(feed): collapse count + facets into one /feed/summary pass (E2 S4, PERF-13)

The FE fired /feed/count (1 pass) + /facets (3 passes) on every filter change =
4 full scans of the subscribed set. New /api/feed/summary does ONE grouped query
(the base filter with tags stripped, GROUP BY channel_id -> per-channel video
counts) and derives the total count + every tag's distinct-channel facet count in
Python on the ~few-hundred-row channel map, faithfully mirroring filtered_query's
channel-based tag logic + the /facets drill-down (own category dropped, unless a
conjunctive topic-AND). Returns {count, facets} — the same numbers the two old
endpoints returned.

FE: a single shared query (Feed reads .count, Sidebar reads .facets); same key +
filters, so React Query dedupes to ONE request. Invalidations repointed to
qk.feedSummary. The old /feed/count + /facets endpoints (and their now-unused FE
api/qk) are kept as the equivalence-test oracle + safety net; a later cleanup can
drop them.

New equivalence test (test_feed_views, 8 filter combos incl. cross-category,
disjunctive/conjunctive topic modes, search): /feed/summary count == /feed/count
and facets == /facets, byte-identical. Structural win: 2 requests / 4-6 queries
-> 1 request / 2-3 queries (the review measured 530 -> 144 ms). Gate green:
344 pytest, frontend tsc/eslint/knip/prettier/222 vitest.

backend/app/routes/feed.py

@@ -13,6 +13,7 @@ from app.db import get_db
 from app.feedquery import (
     decode_cursor,
     encode_cursor,
+    feed_summary,
     filtered_query,
     keyset_predicate,
     order_by,
@@ -174,6 +175,19 @@ def get_facets(
     return {"counts": counts}
 
 
+@router.get("/feed/summary")
+def get_feed_summary(
+    params: dict = Depends(_feed_params),
+    user: User = Depends(current_user),
+    db: Session = Depends(get_db),
+) -> dict:
+    """The sidebar's total video count + per-tag channel facet counts in ONE request and ONE grouped
+    query, replacing the separate /feed/count (1 pass) + /facets (3 passes) the FE fired on every filter
+    change (PERF-13). Response: {"count": <videos>, "facets": {<tag_id>: <channel_count>}} — the same
+    numbers /feed/count's `count` and /facets' `counts` return, so the two are interchangeable."""
+    return feed_summary(db, user, **params)
+
+
 class VideoStateIn(BaseModel):
     status: str