perf(db): the channel manager and the feed sidebar read an index, not the video heap

GET /api/channels summed every subscribed channel's videos by reading each video's heap page
(681 MB on prod): 51-61 ms warm, but 2.25 s on a first open and 6.4 s under EXPLAIN once the
table had left memory. /feed/summary and /feed/years did the same (~140 ms warm, ~800 ms cold).
Migration 0095 replaces ix_videos_channel_pub_desc with the same key INCLUDING the columns
those queries read, so they are Index Only Scans over a 25 MB index. A test holds the queries
and the index's column list together.

The admin Configuration page did a db.get per setting (two for an unset one): it now reads
every override in one query (~40 ms of ~55 on prod).

backend/tests/test_channel_list_index_only.py

@@ -0,0 +1,83 @@
+"""The channel manager's sums and the feed sidebar's counts read the index alone (E31 S4d).
+
+`GET /api/channels` counts each subscribed channel's videos and sums their durations; `/feed/summary`
+and `/feed/years` count the reader's videos per channel and per year under the default filters. They
+used to read every video's heap page for that (681 MB on prod), a 2–6 s first open once something else
+had pushed the table out of memory. Migration 0095 makes `ix_videos_channel_pub_cover` carry every
+column those queries read, so Postgres answers them with Index Only Scans. This test holds the queries
+and the index together: a column added to one and not the other fails it. DB lane.
+"""
+
+import re
+
+from sqlalchemy import text
+from sqlalchemy.dialects import postgresql
+
+from app.feedquery import filtered_query
+from app.models import Video
+from app.routes.channels import channel_aggregates
+
+INDEX = "ix_videos_channel_pub_cover"
+
+# The feed's own defaults (routes/feed.py _feed_params): what the sidebar asks on a plain open.
+FEED_DEFAULTS = {
+    "tags": [],
+    "tag_modes": {"language": "or", "topic": "or", "other": "or"},
+    "untagged": False,
+    "channel_ids": [],
+    "q": None,
+    "min_duration": None,
+    "max_duration": None,
+    "max_age_days": None,
+    "published_after": None,
+    "published_before": None,
+    "show_normal": True,
+    "include_shorts": False,
+    "include_live": False,
+    "show": "unwatched",
+    "scope": "my",
+    "library_source": "organic",
+}
+
+
+def _index_columns(db) -> list[str]:
+    # Key columns first, then the INCLUDE ones, in the index's own order.
+    return list(
+        db.execute(
+            text(
+                "SELECT a.attname FROM pg_index i "
+                "JOIN pg_class c ON c.oid = i.indexrelid "
+                "CROSS JOIN LATERAL unnest(i.indkey) WITH ORDINALITY AS k(attnum, n) "
+                "JOIN pg_attribute a ON a.attrelid = i.indrelid AND a.attnum = k.attnum "
+                "WHERE c.relname = :name ORDER BY k.n"
+            ),
+            {"name": INDEX},
+        ).scalars()
+    )
+
+
+def _video_columns(stmt) -> set[str]:
+    # The columns of `videos` the statement as SENT reads: the compiled SQL, not the expression tree,
+    # which still carries the projection a with_only_columns replaced.
+    sql = str(stmt.compile(dialect=postgresql.dialect()))
+    return set(re.findall(r"\bvideos\.(\w+)", sql))
+
+
+def _assert_covered(db, read: set[str]) -> None:
+    held = _index_columns(db)
+    assert held, f"{INDEX} is missing"
+    # It leads with channel_id, so it also serves every per-channel lookup the old index did.
+    assert held[0] == "channel_id"
+    assert read <= set(held), f"read but not in {INDEX}: {sorted(read - set(held))}"
+
+
+def test_the_channel_sums_read_only_columns_the_index_holds(db):
+    _assert_covered(db, _video_columns(channel_aggregates(["UC_x"])))
+
+
+def test_the_feed_sidebar_counts_read_only_columns_the_index_holds(db, make_user):
+    # feed_summary groups the default filter by channel, feed_years by publish date.
+    base, _rank = filtered_query(db, make_user(), **FEED_DEFAULTS)
+    _assert_covered(
+        db, _video_columns(base.with_only_columns(Video.channel_id, Video.published_at))
+    )