fix(docs-infra): fix API list search color and styles (#31272)

- Add more spacing to inputs.
- Correct placeholder colors in inputs.
- Add aria label to input for accessibility.
- Clean up layout styles and mobile view.

Fixes #31265

PR Close #31272

aio/src/app/custom-elements/api/api-list.component.html

@@ -15,7 +15,7 @@
   </aio-select>
 
   <div class="form-search">
-    <input #filter placeholder="Filter" (input)="setQuery($event.target.value)">
+    <input #filter placeholder="Filter" (input)="setQuery($event.target.value)" aria-label="Filter Search">
     <i class="material-icons">search</i>
   </div>
 </div>