Add check to Lockbud CI job (#6898)

scripts/ci/check-lockbud.sh

@@ -0,0 +1,17 @@
+#!/bin/bash
+
+# Run lockbud to check for deadlocks and capture the output
+output=$(cargo lockbud -k deadlock -b -l tokio_util 2>&1)
+
+# Check if lockbud returned any issues
+if echo "$output" | grep -q '"bug_kind"'; then
+  # Print the JSON payload
+  echo "Lockbud detected issues:"
+  echo "$output"
+
+  # Exit with a non-zero status to indicate an error
+  exit 1
+else
+  echo "No issues detected by Lockbud."
+  exit 0
+fi