The API isn't using the appropriate services for managing forks

What does this MR do?

Modifies fork endpoints to use current fork services

Why was this MR needed?

Because the endpoints are not using the current services and doesn't use the ForkNetworkMember relationships

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 Backend
• Conform by the merge request performance guides
• Conform by the style guides
• Squashed related commits together
• Internationalization required/considered

What are the relevant issue numbers?

Closes #40752 (closed)