Add synonym API examples (#3486)

(cherry picked from commit 83092c8)

Author: lcawl

compiler/src/model/utils.ts

@@ -668,7 +668,7 @@ export function hoistRequestAnnotations (
       const privileges = [
         'all', 'cancel_task', 'create_snapshot', 'grant_api_key', 'manage', 'manage_api_key', 'manage_ccr',
         'manage_enrich', 'manage_ilm', 'manage_index_templates', 'manage_inference', 'manage_ingest_pipelines', 'manage_logstash_pipelines',
-        'manage_ml', 'manage_oidc', 'manage_own_api_key', 'manage_pipeline', 'manage_rollup', 'manage_saml', 'manage_search_application', 'manage_search_query_rules',
+        'manage_ml', 'manage_oidc', 'manage_own_api_key', 'manage_pipeline', 'manage_rollup', 'manage_saml', 'manage_search_application', 'manage_search_query_rules', 'manage_search_synonyms',
         'manage_security', 'manage_service_account', 'manage_slm', 'manage_token', 'manage_transform', 'manage_user_profile',
         'manage_watcher', 'monitor', 'monitor_ml', 'monitor_rollup', 'monitor_snapshot', 'monitor_text_structure',
         'monitor_transform', 'monitor_watcher', 'read_ccr', 'read_ilm', 'read_pipeline', 'read_security', 'read_slm', 'transport_client'