fix(scan): auto-finalize empty scans + system_stats picks running batch with actual work

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

backend/app/api/settings.py

@@ -141,11 +141,23 @@ async def system_stats():
         ).all()
         integrity_counts = {row[0]: row[1] for row in integrity_rows}
 
-        # Active batch (most recent running)
+        # Active batch = running batch that still has outstanding work.
+        # Plain "most recent running" picks a freshly-created scan that
+        # enqueued zero new files and hides the older batch that's
+        # actually being processed; the EXISTS clause filters those
+        # empty batches out.
         active_batch_row = (
             await session.execute(
                 select(ImportBatch)
-                .where(ImportBatch.status == "running")
+                .where(
+                    ImportBatch.status == "running",
+                    select(ImportTask.id)
+                    .where(
+                        ImportTask.batch_id == ImportBatch.id,
+                        ImportTask.status.in_(["pending", "queued", "processing"]),
+                    )
+                    .exists(),
+                )
                 .order_by(ImportBatch.started_at.desc())
                 .limit(1)
             )