Refactor pipeline new form to use controller

What does this MR do?

This MR refactors the recently moved pipeline/new view to Vue. It's currently behind feature flag new_pipeline_form. It was flipped off due to a discrepancy between the API and the controller. Specifically the only values of :api and :web. Which will not allow us to use the public API.

I will have a follow up MR to move over the new pipeline warning messages to Vue and then flip on the flag.

frontend for #231344 (closed)

Screenshots

Does this MR meet the acceptance criteria?

Conformity

• Changelog entry
• 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