Replace synthetics-ct team references with synthetics-managing (DataDog#2571)

Co-authored-by: ci.datadog-api-spec <[email protected]>

Author: api-clients-generation-pipeline[bot]

.generated-info

@@ -1,4 +1,4 @@
 {
-  "spec_repo_commit": "35630f3",
-  "generated": "2025-08-01 18:17:22.417"
+  "spec_repo_commit": "b308db8",
+  "generated": "2025-08-04 15:39:57.539"
 }