Commit to current branch by default in Web IDE E2E tests

What does this MR do?

This backports the changes from EE: https://gitlab.com/gitlab-org/gitlab-ee/merge_requests/15713

It restores the behavior expected by the tests as originally written - to commit to the current branch.

Screenshots

Does this MR meet the acceptance criteria?

Conformity

• [-] Changelog entry for user-facing changes, or community contribution. Check the link for other scenarios.
• [-] Documentation created/updated or follow-up review issue created
• Code review guidelines
• Merge request performance guidelines
• Style guides
• [-] Database guides
• Separation of EE specific content