Implement search-as-you-type form for Pagefind search

Pagefind search uses a more simple search box than we provide for Elastic:

Pagefind	Elastic

Let's uplift Pagefind search to look and function more like Elastic:

• Fetch and show results as you type
• Use the same search form component as Elastic (if this makes sense)

If it's easy to include breadcrumbs with the results, let's do that as well. If not, let's create a follow-up for it. Remember that the breadcrumbs come from metatags on the pages, so we might have to do some work to get those into the Pagefind index.