Oh that's awesome. I think I bumped into it once, but my search flow is usually always in a rush that I haven't had time to stop and think about it.
You can click the "Quick Answer" button on the search results page to trigger the same feature. I think it appears whenever there is more than one word in the search query.
You can also force its appearance by sticking a ? at the end of a query, either space separated or otherwise.
Thanks for linking to the docs. I really like this feature, but as you said, it felt like it showed up at random
Since last week, it will trigger whenever your search query ends with a ? or starts with How or Why or other interrogative words
https://kagi.com/changelog#3179
They disabled the interrogative words trigger because people found it too intrusive. ? still works