fix: align delivered extension UI with the design prototype #13

Parent

Part of #1.

Problem

The built extension implements the core filtering behavior but its visual presentation differs from design/prototype/index.html. The toolbar lacks icons, counter pills and the split-button separator. The menu lacks its product header, descriptions, aligned counts, styled checkboxes and switches. Settings shows all sections together instead of navigating between sections, and uses different cards and rule actions.

Acceptance criteria

• Align the toolbar, menu, notices, labels and empty states with the prototype's component structure, spacing, tokens and icons.
• Align Settings navigation, header, context, preset cards, rule actions and forms with the prototype.
• Preserve accessible names, keyboard interaction, validation and updates across open tabs.
• Check light and dark presentation in the built extension and run all required checks.

Scope

Correct the presentation of delivered features. Open comment highlighting (#9), tree entry hints (#10) and large pull request behavior (#11) retain their existing dependency order.