Moved EE-specific code in `app/view/search/_form.html.haml`

What does this MR do?

Handles conditional rendering for EE-specific code in app/views/search/_form.html.haml with render_if_exists and a subtemplate ee/app/views/search/_form_elasticsearch.html.haml.

This solves issue #11040 (closed)

Does this MR meet the acceptance criteria?

Conformity

• Changelog entry
• Code review guidelines
• Merge request performance guidelines
• Style guides
• Separation of EE specific content

Performance and testing

• Review and add/update tests for this feature/bug. Consider all test levels. See the Test Planning Process.