[Profiling] Remove deprecated methods

[jbcrail]

Summary

This PR removes several methods that are no longer used after migrating to the Elasticsearch plugin.

Removing these methods will also make #165198 and future refactoring easier.

For maintainers

• This was checked for breaking API changes and was labeled appropriately

[apmmachine]

🤖 GitHub comments

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• /oblt-deploy : Deploy a Kibana instance using the Observability test environments.
• /oblt-deploy-serverless : Deploy a serverless Kibana instance using the Observability test environments.
• run elasticsearch-ci/docs : Re-trigger the docs validation. (use unformatted text in the comment!)

[kibana-ci]

💚 Build Succeeded

• Buildkite Build
• Commit: 40b82e3

Metrics [docs]

Module Count

Fewer modules leads to a faster build time

id	before	after	diff
profiling	200	199	-1

Public APIs missing comments

Total count of every public API that lacks a comment. Target amount is 0. Run node scripts/build_api_docs --plugin [yourplugin] --stats comments for more detailed information.

id	before	after	diff
profiling	19	17	-2

Page load bundle

Size of the bundles that are downloaded on every page load. Target size is below 100kb

id	before	after	diff
profiling	21.9KB	21.3KB	-618.0B

Unknown metric groups

API count

id	before	after	diff
profiling	19	17	-2

To update your PR or re-run it, just comment with:
@elasticmachine merge upstream

[cauemarcondes]

@jbcrail I'll make these changes myself directly in my PR if that's ok with you. There'll be too many merge conflicts if you merge this one in.

Done Here 46f7e3d

[jbcrail]

Thanks, sounds good. I'll close this now.