feat(integrity): /api/system/stats exposes integrity counts

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

tests/test_api_settings.py

@@ -80,3 +80,28 @@ async def test_system_stats_shape(client):
         assert key in body
     for status in ("pending", "queued", "processing", "complete", "skipped", "failed"):
         assert status in body["tasks"]
+
+
+@pytest.mark.asyncio
+async def test_system_stats_integrity_counts(client, db):
+    from backend.app.models import ImageRecord
+
+    base = "stats_" + "0" * 56
+    for i, status in enumerate(
+        ["ok", "ok", "corrupt", "failed_verification"]
+    ):
+        db.add(ImageRecord(
+            path=f"/images/i/{i}.jpg", sha256=base + f"{i:02d}",
+            size_bytes=1, mime="image/jpeg", width=1, height=1,
+            origin="imported_filesystem", integrity_status=status,
+        ))
+    await db.commit()
+
+    resp = await client.get("/api/system/stats")
+    assert resp.status_code == 200
+    body = await resp.get_json()
+    integ = body["integrity"]
+    assert integ["ok"] >= 2
+    assert integ["corrupt"] >= 1
+    assert integ["failed_verification"] >= 1
+    assert "unknown" in integ