Use standard tracing headers for distributed tracing

[mshustov]

Requires:

• Implement Elasticsearch query tracing to a source in Kibana #101587
• Switch to APM-based solution for the execution context tracing on the server-side #101627

For the deeper integration with the APM, we should leverage the standard set of tracing headers.

The task can be split into 2 steps:

• Refactor Kibana App < --> Kibana server communication. The initial implementation of Implement Elasticsearch query tracing to a source in Kibana #101587 relies on the kbn-context header to pass async execution context, no transaction is created. Having Provide API for manual Context management  apm-agent-rum-js#1040 is implemented, we can propagate runtime context information to the Kibana server via baggage header.
• Refactor Kibana server < -- > Elasticsearch server communication. In the first iteration, we start with passing execution context to the Elasticsearch server via x-opaque-id header. There is an effort to instrument Elasticsearch server with Java APM client, we will have to switch to the standard tracing headers to provide better integration. blocked by add W3C baggage support apm-agent-nodejs#2102

[elasticmachine]

Pinging @elastic/kibana-core (Team:Core)

[pgayvallet]

Still blocked by elastic/apm-agent-nodejs#2102