polish(home): drop the redundant badge from featured cards, widen the search pill

All four featured posts are case studies, so the badge repeated the same word
four times; the card grid already sits under a 'Featured' heading. Search pill
gets a little horizontal room so 'Search /' does not read as cramped.

src/pages/index.astro

@@ -46,7 +46,6 @@ const featuredPosts = featured.length === 4 ? featured : posts.slice(0, 4);
     <div class="featured-grid">
       {featuredPosts.map((p) => (
         <a class="featured-card" href={`/posts/${p.slug}/`}>
-          <span class="featured-badge">{p.data.category}</span>
           <h3>{p.data.title}</h3>
           <p>{p.data.description}</p>
         </a>