Sustainable Kibana Architecture: Move modules owned by @elastic/logstash (#202756)

## Summary

This PR aims at relocating some of the Kibana modules (plugins and
packages) into a new folder structure, according to the _Sustainable
Kibana Architecture_ initiative.

> [!IMPORTANT]
> * We kindly ask you to:
> * Manually fix the errors in the error section below (if there are
any).
> * Search for the `packages[\/\\]` and `plugins[\/\\]` patterns in the
source code (Babel and Eslint config files), and update them
appropriately.
> * Manually review
`.buildkite/scripts/pipelines/pull_request/pipeline.ts` to ensure that
any CI pipeline customizations continue to be correctly applied after
the changed path names
> * Review all of the updated files, specially the `.ts` and `.js` files
listed in the sections below, as some of them contain relative paths
that have been updated.
> * Think of potential impact of the move, including tooling and
configuration files that can be pointing to the relocated modules. E.g.:
>     * customised eslint rules
>     * docs pointing to source code

> [!NOTE]
> * This PR has been auto-generated.
> * Any manual contributions will be lost if the 'relocate' script is
re-run.
> * Try to obtain the missing reviews / approvals before applying manual
fixes, and/or keep your changes in a .patch / git stash.
> * Please use
[#sustainable_kibana_architecture](https://elastic.slack.com/archives/C07TCKTA22E)
Slack channel for feedback.

#### 1 plugin(s) are going to be relocated:

| Id | Target folder |
| -- | ------------- |
| `@kbn/logstash-plugin` | `x-pack/platform/plugins/private/logstash` |


<details >
<summary>Updated references</summary>

```
./docs/developer/plugin-list.asciidoc
./package.json
./packages/kbn-repo-packages/package-map.json
./packages/kbn-synthetic-package-map/synthetic-packages.json
./packages/kbn-ts-projects/config-paths.json
./tsconfig.base.json
./tsconfig.base.type_check.json
./tsconfig.refs.json
./x-pack/.i18nrc.json
./x-pack/build/plugin/kibana/x-pack/.i18nrc.json
./x-pack/platform/plugins/private/logstash/jest.config.js
./yarn.lock
```

</details><details >
<summary>Updated relative paths</summary>

```
x-pack/platform/plugins/private/logstash/jest.config.js:10
x-pack/platform/plugins/private/logstash/tsconfig.json:3
```

</details>

docs/developer/plugin-list.asciidoc

@@ -711,7 +711,7 @@ using the CURL scripts in the scripts folder.
 |Exposes the shared components and APIs to access and visualize logs.
 
 
-|{kib-repo}blob/{branch}/x-pack/plugins/logstash[logstash]
+|{kib-repo}blob/{branch}/x-pack/platform/plugins/private/logstash[logstash]
 |WARNING: Missing README.