Fix up test scenario 'NoSetupRepoFactory' E2E test

[artaleks9]

Is your task related to a problem? Please describe

The NoSetupRepoFactory E2E test is break an execution for public repositories on the test step Commit the changes, as fail, but it's the expected and correct behavior (update, see the issue [1]). Therefore, in this case, the test should be finished as success. Also the NoSetupRepoFactory has incorrect test steps related to Push the changes, which are no sense.(update, see the issue [1]).

Describe the solution you'd like

• Fix up NoSetupRepoFactory E2E test, that it will be finished on Commit the changes test step, as a successful.
• Fix up RefusedOAuthFactory E2E test, that it will be finished on Commit the changes test step, as a successful.
• Get rid from the incorrect/unnecessary test steps related to Push the changes (update, see the issue [1])

[1] Improve a behavior when try to commit changes for a public repository factory without PAT/OAuth setup

Describe alternatives you've considered

Additional context

Screenshot:

[che-bot]

Issues go stale after 180 days of inactivity. lifecycle/stale issues rot after an additional 7 days of inactivity and eventually close.

Mark the issue as fresh with /remove-lifecycle stale in a new comment.

If this issue is safe to close now please do so.

Moderators: Add lifecycle/frozen label to avoid stale mode.