FTM: New UVE Toolbar - Implement "Experiments" button

[KevinDavilaDotCMS]

Parent Issue

#30598

Task

Integrate the existing Experiments component into the new UVE Toolbar and implement the necessary store logic.
This task involves adapting the newWithEditorToolbar() feature store to support the Experiments functionality in both traditional and headless pages.

Proposed Objective

Successfully integrate the Experiments component into the new toolbar while maintaining its functionality across both traditional and headless pages, ensuring it works correctly under the feature flag.

Acceptance Criteria

• Define the new state object for the new toolbar in newWithEditorToolbar() to support Experiments functionality.
• Integrate the existing Experiments component into the new toolbar UI.
• Implement the necessary store logic to handle Experiments component state and interactions.
• Ensure the Experiments functionality works correctly in both traditional and headless pages.
• Verify that all existing Experiments features work seamlessly within the new toolbar context.
• Test the integration in both traditional and headless page contexts to ensure consistent behavior.

[github-actions]

PRs:

• chore(uve): Add Running Experiments Badge to new toolbar #30824