It can be done using this method.
For a featured section you could create a “Featured” category and put the shortcode on the page twice. The first one limited to the “Featured” category and the second for general results. If you do, the lock shortcode option could be useful in order to make sure the “locked” shortcode instance is not effect by search and category selection choice made by the user. The downside is that the featured instance would be shown on on the single entry page too. One way around that would be to create a “Results” page and direct the links to it with the home_id. On the “Results” page you would just use the
[connections] shortcode with no options. You could get creative though and use the template shortcode option on the page so the results are shown in a different template.
I hope that isn’t confusing and makes sense.