Add the ability to cherry pick accross forks [RUN ALL RSPEC] [RUN AS-IF-FOSS]

What does this MR do?

Adds the ability to cherry-pick across forks.

Note: this feature is behind the :pick_into_project feature flag.

TODO

• Create rollout issue

Screenshots (strongly suggested)

Does this MR meet the acceptance criteria?

Conformity

• 📋 Does this MR need a changelog?
  • I have included a changelog entry.
• Documentation (if required)
• Code review guidelines
• Merge request performance guidelines
• Style guides

Availability and Testing

• Review and add/update tests for this feature/bug. Consider all test levels. See the Test Planning Process.
• Tested in all supported browsers

Related to #21268 (closed)