We experience the same issue but with 8.0.0 (this was a fresh install, no clue what happened than).
For trial&error reasons I gave my user at least every single role available, but didn't work out.
ES logs are clean, Kibana log throws:
[2022-03-16T18:29:56.233+00:00][ERROR][plugins.monitoring.monitoring] ResponseError: security_exception: [security_exception] Reason: action [indices:data/read/search] is unauthorized for user [hauke] with roles [superuser,kibana_admin,monitoring_user,editor,machine_learning_user,remote_monitoring_collector,snapshot_user,transport_client,watcher_user,beats_admin,ingest_admin,logstash_admin,machine_learning_admin,rollup_admin,transform_admin,watcher_admin,apm_system,beats_system,kibana_system,logstash_system,viewer,transform_user,enrich_user,remote_monitoring_agent,rollup_user], this action is granted by the index privileges [read,all]
Monitoring indices are indeed there and get also new docs.
Edit: We are also on only one cluster, no dedicate monitoring cluster.