EE port of "Add e2e QA test for logging in using Github OAuth"

What does this MR do?

EE port of https://gitlab.com/gitlab-org/gitlab-ce/merge_requests/24817

What are the relevant issue numbers?

#56489

Does this MR meet the acceptance criteria?

• [-] Changelog entry added, if necessary
• [-] Documentation created/updated via this MR
• [-] Documentation reviewed by technical writer or follow-up review issue created
• Tests added for this feature/bug
• [-] Tested in all supported browsers
• Conforms to the code review guidelines
• Conforms to the merge request performance guidelines
• Conforms to the style guides
• Conforms to the database guides
• [-] Link to e2e tests MR added if this MR has Requires e2e tests label. See the Test Planning Process.
• [-] EE specific content should be in the top level /ee folder
• [-] For a paid feature, have we considered GitLab.com plans, how it works for groups, and is there a design for promoting it to users who aren't on the correct plan?
• [-] Security reports checked/validated by reviewer