Inherit StagesController from Projects::Pipelines::ApplicationController

MR StagesController

Part of #220605 (comment 365746942)

What does this MR do?

This MR refactors our StagesController to use our new Pipeline Abstract Controller introduced in !34410 (merged).

It includes the following items:

• Refactor StagesController to inherit from Projects::Pipelines::ApplicationController
• Refactor its associated route
• Refactor its spec

endpoint before	endpoint after
/*namespace_id/:project_id/-/pipelines/:id/stages/:stage_name/play_manual(.:format)	/*namespace_id/:project_id/-/pipelines/:pipeline_id/stages/:stage_name/play_manual(.:format)

Why are we doing this?

Our StagesController is currently inheriting from PipelinesController which has a set of actions and operations that should not be exposed to child controllers. This MR makes sure we don't leak those actions.

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