fix(search): every related and live-search request takes a slot, and a failed one gives it back

A related list's cursor cost nothing, and a cursor is a free string: a replayed one read and
enriched without end. Every request now takes a slot of the user's daily cap — taken under a lock
before the work (`quota.claim_action`), so requests sent together cannot all pass the last free
one, and given back when the request fails outright (`quota.refund_action`). The live search's
scrape source takes its slots the same way.

A limit of 0 turns the feature off: a distinct 409 `related_disabled` / `search_disabled`, and
`/api/me` says `related_enabled` / `search_enabled` so the UI can leave it out.

A videos.list that fails no longer reads as an empty page: `ingest_candidates` raises, and the
search and the related list answer the refusal (the shared budget spent says "quota") instead of
"no results". The two routes' page loops are one (`_gather`).

`clear` deletes only what the caller found: a related list's rows carry no find, and any user
could name them.

backend/tests/test_search_cap.py

@@ -0,0 +1,132 @@
+"""`GET /api/search/youtube` — the per-user daily cap of the live search (scrape source).
+
+The scrape is replaced by pages the test hands out, and YouTube's videos.list by an offline enrich.
+What is held: every request takes a slot, a cursor's too; a search that failed outright gives its
+slot back; a zero limit turns live search off, which says so instead of "try again tomorrow"; and a
+lookup that fails says why instead of answering "no results"."""
+
+import pytest
+
+from app import quota, sysconfig
+from app.routes import search as search_routes
+from app.youtube.client import YouTubeError
+from app.youtube.innertube import ScrapeError
+
+ACTION = quota.QuotaAction.VIDEOS_SEARCH
+
+
+def _item(n: int) -> dict:
+    return {
+        "id": f"srch{n:07d}",
+        "channel_id": "UCsearch001",
+        "channel_title": "Chan",
+        "title": f"Found {n}",
+        "published_at": None,
+        "thumbnail_url": None,
+        "live_broadcast": "none",
+    }
+
+
+class _FakeYT:
+    fail_videos = False
+
+    def __init__(self, *_a, **_kw):
+        pass
+
+    def __enter__(self):
+        return self
+
+    def __exit__(self, *exc):
+        return False
+
+    def get_channels(self, ids):
+        return []
+
+    def get_videos(self, ids):
+        if _FakeYT.fail_videos:
+            raise YouTubeError("videos -> 403", reason="quotaExceeded", path="videos")
+        return [
+            {
+                "id": i,
+                "snippet": {"title": f"T {i}", "publishedAt": "2025-01-01T00:00:00Z"},
+                "contentDetails": {"duration": "PT30M"},
+                "statistics": {},
+                "status": {},
+            }
+            for i in ids
+        ]
+
+
+@pytest.fixture
+def pages(monkeypatch, db):
+    """The scrape answers with the pages in `state["pages"]`, one per call."""
+    sysconfig.set_value(db, "shorts_probe_max_seconds", 60)
+    sysconfig.set_value(db, "search_source", "scrape")
+    state: dict = {"pages": [], "calls": 0}
+
+    def search(term, continuation=None):
+        state["calls"] += 1
+        page = state["pages"].pop(0)
+        if isinstance(page, Exception):
+            raise page
+        return page
+
+    monkeypatch.setattr(search_routes.search_scrape, "search", search)
+    monkeypatch.setattr(search_routes, "YouTubeClient", _FakeYT)
+    monkeypatch.setattr(_FakeYT, "fail_videos", False)
+    return state
+
+
+def _page(n: int) -> dict:
+    return {"items": [_item(n)], "next_page_token": None}
+
+
+def test_every_request_takes_a_slot_a_cursors_too(db, make_user, as_user, pages):
+    user = make_user()
+    sysconfig.set_value(db, "search_daily_limit_per_user", 1)
+    pages["pages"] = [_page(1), _page(2)]
+    client = as_user(user)
+    assert client.get("/api/search/youtube?q=cats").status_code == 200
+    refused = client.get("/api/search/youtube?q=cats&cursor=more")
+    assert refused.status_code == 429
+    assert refused.json()["detail"]["reason"] == "search_daily_limit"
+    assert pages["calls"] == 1
+
+
+def test_a_search_that_failed_gives_its_slot_back(db, make_user, as_user, pages):
+    user = make_user()
+    sysconfig.set_value(db, "search_daily_limit_per_user", 1)
+    pages["pages"] = [ScrapeError("blocked"), _page(1)]
+    client = as_user(user)
+    assert client.get("/api/search/youtube?q=cats").status_code == 422
+    assert quota.actions_today(db, user.id, ACTION) == 0
+    assert client.get("/api/search/youtube?q=cats").status_code == 200
+    assert quota.actions_today(db, user.id, ACTION) == 1
+
+
+def test_a_zero_limit_turns_live_search_off(db, make_user, as_user, pages):
+    user = make_user()
+    sysconfig.set_value(db, "search_daily_limit_per_user", 0)
+    resp = as_user(user).get("/api/search/youtube?q=cats")
+    assert resp.status_code == 409
+    assert resp.json()["detail"] == {"code": "refused", "reason": "search_disabled"}
+    assert pages["calls"] == 0
+
+
+def test_a_zero_limit_turns_the_api_source_off_too(db, make_user, as_user, pages):
+    user = make_user()
+    sysconfig.set_value(db, "search_source", "api")
+    sysconfig.set_value(db, "search_daily_limit_per_user", 0)
+    resp = as_user(user).get("/api/search/youtube?q=cats")
+    assert resp.status_code == 409
+    assert resp.json()["detail"]["reason"] == "search_disabled"
+
+
+def test_a_lookup_that_fails_says_why_not_no_results(db, make_user, as_user, pages, monkeypatch):
+    user = make_user()
+    monkeypatch.setattr(_FakeYT, "fail_videos", True)
+    pages["pages"] = [_page(1)]
+    resp = as_user(user).get("/api/search/youtube?q=cats")
+    assert resp.status_code == 422
+    assert resp.json()["detail"] == {"code": "youtube", "reason": "quota"}
+    assert quota.actions_today(db, user.id, ACTION) == 0