Core Elasticsearch: remove "data" and "admin" clients and expose single client

[rudolf]

For "tribe mode" support, we used to expose two elasticsearch clients a "data" and "admin" client. Since Kibana no longer supports "tribe mode" Core should expose a single Elasticsearch client.

[elasticmachine]

Pinging @elastic/kibana-platform (Team:Platform)

[joshdover]

With the proposal to add the new Elasticsearch.js client alongside the existing clients in #35508, I think this work may be unnecessary churn. There's no increased maintenance burden in continuing to support both adminClient and dataClient. It seems we can just remove both of these once we decide to drop support for the legacy client, no?

[rudolf]

Yeah this is probably low priority and can be done as part of #35508. I think the cost is more on the API consumer side, it adds confusion and two ways to do the same thing.