How to Get The Excerpt of the page that displays Blog Posts

You can use get_queried_object() to get the static page data, and then do something like so to get the excerpt of the page:

echo get_the_excerpt( get_queried_object() );

// Or to apply filters just as the_excerpt() does:
$excerpt = get_the_excerpt( get_queried_object() );
echo apply_filters( 'the_excerpt', $excerpt );