Backport changes from gitlab-ee!6740

What does this MR do?

Moves some code around to make it more extendable in EE and re-styles the project templates:

Screenshots (if relevant)

Before	After

Does this MR meet the acceptance criteria?

• Changelog entry added, if necessary
• Documentation created/updated
• API support added
• Tests added for this feature/bug
• Conforms to the code review guidelines
  • Has been reviewed by a UX Designer
  • Has been reviewed by a Frontend maintainer
  • Has been reviewed by a Backend maintainer
  • Has been reviewed by a Database specialist
• Conforms to the merge request performance guidelines
• Conforms to the style guides
• Conforms to 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-ee/issues/6860