[8.16](backport #4333) [apm] Update APM docs to reflect changes related to the Elasticsearch apm-data plugin

[mergify]

Description

Updates APM docs to reflect changes related to the Elasticsearch apm-data plugin.

Here's my understanding of how this change will impact the docs (please correct me if I'm wrong!):

1️⃣ When a user sets up the APM Server binary, they used to have to install the APM integration. Now users using the APM Server binary shouldn't have to install or work with the APM integration at all because the functionality that the APM integration was providing to the APM Server binary users is now built into Elasticsearch (i.e. the apm-data plugin) (if I'm understanding elastic/apm-server#11267 correctly).

2️⃣ When a user sets up a Fleet-managed APM Server, how the APM integration works behind the scenes changes with the addition of the Elasticsearch apm-data plugin, but the workflow for getting a Fleet-managed APM Server initially set up will not change so the docs on getting set up don't need to be updated.

3️⃣ Users using either the APM Server binary or Fleet-managed APM Server will need to know about how the Elasticsearch apm-data plugin works and how the APM integration's role has changed if/when they are customizing index templates, component templates, or ingest pipelines.

4️⃣ In addition to updates in the Observability guide, the integration docs probably also need to be updated.

Preview: https://observability-docs_bk_4333.docs-preview.app.elstc.co/guide/en/observability/master/apm.html

Documentation sets edited in this PR

Check all that apply.

• Stateful (docs/en/observability/*)
• Serverless (docs/en/serverless/*)
• Integrations Developer Guide (docs/en/integrations/*)
• None of the above

Related issue

Closes #4313

Checklist

• Initial updates
  • Search APM +\n?integration
  • Search data *\n?streams?
  • Search index +\n?templates?
  • Search index +\n?mappings?
  • Search ILM +\n?polic(y|ies)
  • Search ingest +\n?pipelines?
• Decide if it should be "Elasticsearch APM data plugin" or "Elasticsearch apm-data plugin" and then make sure we're using one phrase consistently
• Product/Engineering Review
• Writer Review

Follow-up tasks

Select one.

• This PR does not need to be ported to another doc set because:
  • The concepts in this PR only apply to one doc set (serverless or stateful)
  • The PR contains edits to both doc sets (serverless and stateful)
• This PR needs to be ported to another doc set:
  • Port to stateful docs: <link to PR or tracking issue>
  • Port to serverless docs: [Request]: Port #4333 to serverless docs #4420

---

This is an automatic backport of pull request #4333 done by [Mergify](https://mergify.com).

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