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/tests/test_feed_views.py

@@ -9,7 +9,9 @@ Regression nets for two query rewrites that must stay behaviour-equivalent:
 """
 from datetime import datetime, timezone
 
-from app.models import Channel, Subscription, Video, VideoState
+import pytest
+
+from app.models import Channel, ChannelTag, Subscription, Tag, Video, VideoState
 
 
 def _dt(day: int) -> datetime:
@@ -82,3 +84,64 @@ def test_watch_state_views_return_the_right_sets(db, as_user, make_user):
     assert _feed_ids(client, "show=unwatched") == {"vProg", "vNew"}
     # "all" shows everything except hidden
     assert _feed_ids(client, "show=all") == {"vWatch", "vProg", "vNew"}
+
+
+def _seed_tagged(db, make_user):
+    """A user subscribed to 4 channels with a spread of language/topic/other tags and differing video
+    counts, so the count sum and the per-category facet drill-down are all non-trivial."""
+    user = make_user(email="summary@example.com")
+    tags = {
+        "L1": Tag(user_id=None, name="Hungarian", category="language"),
+        "L2": Tag(user_id=None, name="English", category="language"),
+        "T1": Tag(user_id=None, name="Tech", category="topic"),
+        "T2": Tag(user_id=None, name="Gaming", category="topic"),
+        "O1": Tag(user_id=None, name="Favourite", category="other"),
+    }
+    db.add_all(tags.values())
+    chans = {c: Channel(id=c, title=c, subscriber_count=10) for c in ("chA", "chB", "chC", "chD")}
+    db.add_all(chans.values())
+    db.flush()
+    # channel -> tag keys
+    links = {"chA": ["L1", "T1"], "chB": ["L1", "T2"], "chC": ["L2", "T1", "O1"], "chD": []}
+    for cid, tkeys in links.items():
+        db.add(Subscription(user_id=user.id, channel_id=cid, priority=0, hidden=False))
+        for tk in tkeys:
+            db.add(ChannelTag(channel_id=cid, tag_id=tags[tk].id, user_id=None))
+    # differing video counts per channel (chA:3, chB:2, chC:1, chD:2)
+    counts = {"chA": 3, "chB": 2, "chC": 1, "chD": 2}
+    for cid, n in counts.items():
+        db.add_all([_video(f"{cid}v{i}", cid, f"{cid} clip {i}") for i in range(n)])
+    db.commit()
+    return user, {k: v.id for k, v in tags.items()}
+
+
+# Query-param combos (as a template with {L1}/{T1}/… placeholders) that stress every facet path:
+# no tags, single-category, cross-category, disjunctive + conjunctive topic modes, and a search filter.
+_SUMMARY_CASES = [
+    "show=all",
+    "show=all&tags={L1}",
+    "show=all&tags={T1}",
+    "show=all&tags={L1}&tags={T1}",
+    "show=all&tags={T1}&tags={T2}&tag_mode=or",
+    "show=all&tags={T1}&tags={T2}&tag_mode=and",
+    "show=all&q=clip",
+    "show=unwatched",
+]
+
+
+@pytest.mark.parametrize("case", _SUMMARY_CASES)
+def test_feed_summary_matches_count_plus_facets(db, as_user, make_user, case):
+    # /feed/summary must return byte-identical numbers to the old /feed/count + /facets it replaces,
+    # across the full matrix of tag filters — it reimplements the tag drill-down in Python, so this is
+    # the equivalence net.
+    user, tag_ids = _seed_tagged(db, make_user)
+    client = as_user(user)
+    qs = case.format(**tag_ids)
+
+    summary = client.get(f"/api/feed/summary?{qs}")
+    count = client.get(f"/api/feed/count?{qs}")
+    facets = client.get(f"/api/facets?{qs}")
+    assert summary.status_code == count.status_code == facets.status_code == 200
+
+    assert summary.json()["count"] == count.json()["count"], qs
+    assert summary.json()["facets"] == facets.json()["counts"], qs