WIP: Redesign Project Integrations page

What does this MR do?

Redesigns Project Integrations page based on specifications provided in https://gitlab-org.gitlab.io/gitlab-design/hosted/pedro/ce%2334059-spec-previews/

Screenshots (TBA)

Does this MR meet the acceptance criteria?

• Changelog entry added, if necessary
• [ ] Documentation created/updated
• [ ] API support added
• Tests added for this feature/bug
• Review
  • Has been reviewed by UX
  • Has been reviewed by Frontend
  • Has been reviewed by Backend
  • [ ] Has been reviewed by Database
• Conform by the merge request performance guides
• Conform by the style guides
• Squashed related commits together

What are the relevant issue numbers?

Closes #34059 (moved)