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

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

backend/app/api/settings.py

@@ -83,6 +83,17 @@ async def system_stats():
         ).all()
         status_counts = {row[0]: row[1] for row in status_rows}
 
+        # Integrity counts — FC-2e.
+        integrity_rows = (
+            await session.execute(
+                select(
+                    ImageRecord.integrity_status,
+                    func.count(ImageRecord.id),
+                ).group_by(ImageRecord.integrity_status)
+            )
+        ).all()
+        integrity_counts = {row[0]: row[1] for row in integrity_rows}
+
         # Active batch (most recent running)
         active_batch_row = (
             await session.execute(
@@ -116,5 +127,13 @@ async def system_stats():
             "skipped": status_counts.get("skipped", 0),
             "failed": status_counts.get("failed", 0),
         },
+        "integrity": {
+            "unknown": int(integrity_counts.get("unknown", 0)),
+            "ok": int(integrity_counts.get("ok", 0)),
+            "corrupt": int(integrity_counts.get("corrupt", 0)),
+            "failed_verification": int(
+                integrity_counts.get("failed_verification", 0)
+            ),
+        },
         "active_batch": active_batch,
     })