Improve release process docs

What does this MR do?

This MR updates the release process docs in the readme file to reflect the latest UI changes in the New Release page

What are the relevant issue numbers?

No issue number

Does this MR meet the acceptance criteria?

• [-] Changelog entry added
• Documentation created/updated for GitLab EE, if necessary
• Documentation created/updated for this project, if necessary
• Documentation reviewed by technical writer or follow-up review issue created
• Tests added for this feature/bug
• Job definition updated, if necessary
  • Auto-DevOps template
  • Job definition example
  • CI Templates
• Conforms to the code review guidelines
• Conforms to the Go guidelines
• Security reports checked/validated by reviewer