Cache /search/count requests in the browser

What does this MR do?

These requests are typically loaded by the same user repeatedly as they switch tabs on the search page. Considering that Elasticsearch indexing is only updated every 1-2 minutes anyway the 1 minute browser side cache shouldn't really be noticeable to users except for loading counts faster.

This is also using a private cache (default for expires_in) so that it is not cached by intermediate proxies. This is important since each user's permissions is considered in a search.

Screenshots (strongly suggested)

Does this MR meet the acceptance criteria?

Conformity

• Changelog entry
• [-] Documentation (if required)
• Code review guidelines
• Merge request performance guidelines
• Style guides
• Database guides
• Separation of EE specific content

Availability and Testing

• Review and add/update tests for this feature/bug. Consider all test levels. See the Test Planning Process.
• Tested in all supported browsers
• Informed Infrastructure department of a default or new setting change, if applicable per definition of done

Security

If this MR contains changes to processing or storing of credentials or tokens, authorization and authentication methods and other items described in the security review guidelines:

• Label as security and @ mention @gitlab-com/gl-security/appsec
• The MR includes necessary changes to maintain consistency between UI, API, email, or other methods
• Security reports checked/validated by a reviewer from the AppSec team

Related to #300150 (closed)