Replace custom search input with SearchInput component (built-in clear
button) and add 300ms debounce. Fix template card: use Tailwind token
for icon background, fix Badge to use children with badge-s class and
uppercase, match empty-tag fallback height to badge size.
Migrate all icon usage in the skill directory from @remixicon/react
and custom SVG components to Tailwind CSS icon classes (i-ri-*, i-custom-*).
Update MenuItem API to accept string class names instead of React.ElementType.