Revert "Log push output on exception" because it is no longer needed

What does this MR do?

We have successfully diagnosed https://gitlab.com/gitlab-org/gitlab-ce/issues/48241, so this logging is no longer needed.

Does this MR meet the acceptance criteria?

• Changelog entry added, if necessary
• Documentation created/updated
• API support added
• Tests added for this feature/bug
• Conform by the code review guidelines
  • Has been reviewed by a Backend maintainer
• Conform by the [merge request performance guides](https://docs.gitlab.com/ee/development/merge_request_performance_guidelines.html)
• Conform by the style guides
• Conform by the database guides
• If you have multiple commits, please combine them into a few logically organized commits by squashing them
• Internationalization required/considered
• End-to-end tests pass (package-and-qa manual pipeline job)

What are the relevant issue numbers?

https://gitlab.com/gitlab-org/gitlab-ce/issues/48241