Serve /health and keep 404 scanner noise out of the log file

Something on the network polls /health (and /v1/models) every 30 seconds;
the former now answers 200 with a database check instead of a 404, and
django.request is limited to ERROR in the logging config so scanner 404s
stop filling backend/logs/j621.log. Real server errors still log, and the
dev server keeps printing every request to its console.

backend/apps/core/views.py

@@ -1,6 +1,7 @@
 import time
 
 from django.conf import settings
+from django.db import connection
 from rest_framework.exceptions import PermissionDenied
 from rest_framework.permissions import AllowAny, IsAuthenticated
 from rest_framework.response import Response
@@ -66,3 +67,22 @@ class StatsView(APIView):
                 "log": stats.log_tail(),
             }
         )
+
+
+class HealthView(APIView):
+    """Unauthenticated liveness probe for uptime monitors (hits /health)."""
+
+    permission_classes = [AllowAny]
+    authentication_classes = []
+
+    def get(self, request):
+        database = True
+        try:
+            with connection.cursor() as cursor:
+                cursor.execute("SELECT 1")
+        except Exception:  # noqa: BLE001 - report the failure, do not crash
+            database = False
+        return Response(
+            {"status": "ok" if database else "degraded", "database": database},
+            status=200 if database else 503,
+        )