Simplify API Fuzzing CI templates

What does this MR do?

We are simplifying the API Fuzzing CI template to make it easier for users to override and extend the jobs. This is also brings the API Fuzzing template closer to the DAST template.

• Add a latest version of template
• Move script content into actual scripts in the container
• Use SECURE_ANALYZERS_PREFIX in image path
• Latest template has breaking changes as we get ready to deprecate variables in 14.0.
• Latest template (breaking):
  • Remove use of FUZZAPI_REPORT_ASSET_PATH, FUZZAPI_REPORT, FUZZAPI_LOG_SCANNER
  • Remove stages
  • Remove docker-in-docker option
  • Move variable defaults into entry script

Screenshots (strongly suggested)

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

Related to #326165 (closed)