After further struggles with getting the actual ES logs (which is not that simple on hosted ES clusters at elastic.io!!) - I finally was able to access them and noticed many of the following WARNings:
16:32:50.998
elasticsearch.server
[elasticsearch.server][WARN] Authentication to realm found failed - Password authentication failed for ec-local-beats-monitor
I'm not sure who this user might be: "ec-local-beats-monitor" ?? and where it is configured/set - definitely not in my filebeat.yml config for the Filebeat process...
Could this be related to the issue with loosing/ not indexing Filebeat metrics data into ES?