What does this MR do?

A search feature is being added to the group billable members page (issue here). This backend MR updates the group/:id/billable_members endpoint, which is currently used to retrieve the entire list of billable group members.

The search params defined in this MR are based on the proposed design.

No changelog provided as we're hiding that new feature behind the api_billable_member_list feature flag (see related issue)

Finally a frontend MR will follow this one here.

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 #262875 (closed)