chore: migrate from ESLint + Prettier to Biome

- Install @biomejs/biome@2.3.8 as the unified linter and formatter
- Create biome.json with project-specific configuration:
  - Disable a11y rules (not in original ESLint config)
  - Configure rules to match original ESLint behavior
  - Enable Tailwind CSS directive support in CSS parser
  - Add overrides for src/components/ui/** (shadcn components)
- Update package.json scripts: lint, lint:fix, format, format:check
- Update next.config.ts to disable ESLint during builds
- Remove eslint.config.mjs and .prettierrc.json
- Update CONTRIBUTING.md to reference Biome instead of ESLint/Prettier
- Format entire codebase with Biome
- Fix noEmptyPattern error in rate-limit-dashboard.tsx

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Co-Authored-By: Claude <noreply@anthropic.com>