Support API requests in Performance Bar

What does this MR do?

This MR adds Peek support for our Grape endpoints.

It sets the peek_enabled flag in the RequestStore before each request just like we do in our controllers.

Then we persist Peek data manually after each request because Peek only does this for Rails controllers but not for Grape endpoints.

Related to #33909 (closed)

Testing manually

1. Click the plus button on the performance bar
2. Type in a request ID or URL of an API call
3. You should see the queries and other info in the performance bar

Screenshots

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