Remove stages definition from latest API Fuzzing CI template

What does this MR do?

Remove stages definition from latest API Fuzzing CI template.

• Create new latest version of CI template
• Copy and update spec

Related to #326065 (closed)

CI Template

• Breaking changes put into latest version of CI template

• Tests added and updated to include removal of stages

• Corresponding release post

• Test project

  • Project
  • CI template
  • Job

  

Screenshots (strongly suggested)

Latest CI templates do not display in GitLab UX.

Does this MR meet the acceptance criteria?

Conformity

• 📋 Does this MR need a changelog?
  • I have included a changelog entry.
  • I have not included a changelog entry because _____.
• [-] Documentation (if required)
• Code review guidelines
• Merge request performance guidelines
• Style guides
• [-] Database guides
• Separation of EE specific content

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
• [-] Informed Infrastructure department of a default or new setting change, if applicable per definition of done

Security

If this MR contains changes to processing or storing of credentials or tokens, authorization and authentication methods and other items described in the security review guidelines:

• [-] Label as security and @ mention @gitlab-com/gl-security/appsec
• [-] The MR includes necessary changes to maintain consistency between UI, API, email, or other methods
• [-] Security reports checked/validated by a reviewer from the AppSec team