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/scripts/test-aio-a11y.js

@@ -21,7 +21,7 @@ sh.set('-e');
 // Constants
 const MIN_SCORES_PER_PAGE = {
   '': 100,
-  'api': 90,
+  'api': 100,
   'api/core/Directive': 90,
   'cli': 91,
   'cli/add': 91,