chore(atomic): migrate atomic-automatic-facet to Lit

[Copilot]

✅ Checklist

• 🧪 The component is unit tested
• 🧪 The component includes E2E tests
• 🗑️ Old Cypress tests exclusive to the component are removed
• 📖 The component is documented in storybook with an .mdx file
• ♿ The component complies with the Web Content Accessibility Guidelines.
• 🌐 All strings intended for humans or assistive technology must be localized with i18n.
• 📦 The Lit component is exported in the appropriate index.ts and lazy-index.ts files.
• 🎨 CSS parts are documented still accessible.
• 🦥 Slotted Content, public methods and properties are documented
• 🔄 The component outputs the same Angular output as before with Stencil
• 🏷️ The component declares the component type in the HTMLElementTagNameMap

https://coveord.atlassian.net/browse/KIT-[____]

fix #6413

Description

Migrates the atomic-automatic-facet component from Stencil to Lit. This component is a specialized facet generated by the automatic facets feature and is used internally by atomic-automatic-facet-generator.

Changes Made

Component Migration

• Converted component from Stencil (.tsx) to Lit (.ts) with Tailwind CSS styling
• Moved component from facets/atomic-automatic-facet/ to top-level atomic-automatic-facet/ directory in /search folder
• All imports converted to @/* path aliases
• Replaced JSX with html template literals and Lit directives (when, nothing)
• Applied proper Lit decorators (@customElement, @bindings(), @withTailwindStyles)

Testing

• Created buildFakeAutomaticFacet test fixture
• Added comprehensive Vitest unit tests (300+ lines) covering all functionality
• Added minimalist golden path E2E tests with Playwright:
  • Page object model for component interactions
  • Test fixtures for test setup
  • 4 golden path test cases covering rendering, value selection, and clearing
• Analyzed and migrated 12 Cypress test scenarios
• Removed Cypress test files (170+ lines)
• Improved test organization by grouping shadow part tests under descriptive blocks
• Removed duplicate test cases

Documentation

• Added .mdx file documenting internal nature, shadow parts, and generator relationship
• Added Storybook stories for component demonstration

Updated Files

• Updated React wrapper to export the migrated component
• Added test fixtures for the automatic facet controller
• Updated component exports in index.ts and lazy-index.ts

Testing

• ✅ All unit tests pass
• ✅ E2E tests validate golden path scenarios
• ✅ Linting passes
• ✅ Build succeeds without errors
• ✅ Component maintains same API and behavior as Stencil version

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[alexprudhomme]

@copilot Add straight forward minimalist golden path e2e tests. Thanks

[Copilot]

@copilot Add straight forward minimalist golden path e2e tests. Thanks

Added minimalist golden path E2E tests in commit a163594. The tests cover:

• Rendering automatic facet with label
• Displaying facet values
• Selecting facet values
• Clearing selected values

Files created:

• e2e/page-object.ts - Page object model with locators
• e2e/fixture.ts - Test fixture
• e2e/atomic-automatic-facet.e2e.ts - 4 golden path test cases

[fbeaudoincoveo]

I honestly have nothing to