Modernize admin UI to use React and WP components

[jeffpaul]

What problem does this address?

The plugin currently uses a legacy PHP-based admin settings experience. In alignment with the recommendations from core ticket #64308, let's look to update the plugin’s admin interfaces (provider selection, experiment toggles, and other admin-side functionality) to use the modern WP design system and React-based components.

What is your proposed solution?

• Replace the current PHP-rendered settings UI with a React implementation that leverages the @wordpress/components package.
• Follow the patterns and styling defined in the official Figma Design Library and ensure consistency with the Site Editor and other canonical plugins.
• Refactor admin screens for: Provider selection and configuration
• Refactor admin screens for: Experiment toggles and descriptions
• Refactor admin screens for: Any future experiment settings or diagnostics interfaces
• Update plugin documentation to note that all new and updated UIs should be built using React and the WordPress Components design system.
• Reference prior examples such as Preferred Languages PR #546 as implementation guidance.

[jeffpaul]

Let's make sure whoever picks this up also includes #35 in their effort.