How to create a Search API search box that redirects you to the search page
There was a similar question for Drupal 7 Expose a view&#39;s filters both in a block, and in the actual view. In Drupal 8 this should be much easier, you can do this in UI:

Place the block Exposed form: search_content-page_1 a second time, now in the region Content above the block Main page content and configure the visibility to show only on pages with the path /search/content.