[Logs UI] Replace legacy elasticsearch client usage

[weltenwort]

Summary

With the removal of the legacy Elasticsearch client in the Kibana Platform, we need to replace all usage with calls to the data plugin's search or with the new client as described in the migration guide.

[elasticmachine]

Pinging @elastic/logs-metrics-ui (Team:logs-metrics-ui)

[jasonrhodes]

@weltenwort correct me if I'm wrong, but if we're moving to the data plugin in the client and using search strategies, we will no longer need to worry about this migration, right? See: #76677

[weltenwort]

That should cover most of it, yes. To be sure I'd still recommend to search through our plugin codebase, though.

[joshdover]

I'm doing an audit today on where we are on #83910 and it appears that there are no longer any usages of the legacy client in the infra plugin. Could someone confirm and if so, close this issue and update the table in #83910?

Thanks all!

[joshdover]

Scratch that, I did find a few legacy usages in this file: https://github.com/elastic/kibana/blob/master/x-pack/plugins/infra/server/lib/log_analysis/log_entry_categories_analysis.ts

[joshdover]

@jasonrhodes could we get these last bits prioritized? Should be a pretty small lift to get this closed.

[jasonrhodes]

@sgrodzicki I think we should just knock this out ASAP when @weltenwort or @Kerry350 have some bandwidth in between other tasks, since this should be pretty small.