The Use an Existing Question sub-tab permits you to pin an existing question to your site. You can find an engagement question using a question ID or by searching for the text of the question.
I wanted to ask a question with the words dog and/or cat, so I entered "dog cat" and hit Enter.
I selected the second item, question ID 184438. The question was displayed in the widget admin so I could see its answer options and make sure they suit my purpose.
Select Page-Level Engagement to pin the question to this page or General Engagement to use it on any page that shows this target, then hit Submit.