FTM: New UVE Toolbar - Implement "API" button

[KevinDavilaDotCMS]

Parent Issue

#30598

Task

Implement the logic for the "API" button in the new UVE Toolbar component. This task involves modifying (if necessary) store logic for the newWithEditorToolbar() feature store, reusing existing API functionality where possible.

Proposed Objective

Add the "API" button logic to the new toolbar and ensure it functions correctly under the feature flag, maintaining consistency with the existing copy URL functionality.

Acceptance Criteria

• Ensure the "API" button functions correctly and integrates seamlessly with the new toolbar, in traditional and headless pages
• The behavoiur of the current "API" button should not be affected