[Frontend] Mirror changes from Web IDE to CI runner

Frontend Issue for: https://gitlab.com/gitlab-org/gitlab-ee/issues/5276

Please refer to the description of the parent issue for up-to-date information.

This issue was created to track Frontend weight independently of Backend.

Some details

This issue will require the FE to use a backend-provided API to keep runner in sync with the changes on the Web IDE, one way only.