Do those Taoist and Buddhist fortune-telling insights really exist?

Fortune-telling is not enlightened. The Buddha clearly said in the "Teaching Legacy": "Do not occupy each other, look up at the stars, push the surplus and deficiency, and count." In some temples, these things are actually not allowed in Buddhism, which has explicit provisions. However, there are many interests involved, so it's hard to say. If you want to know what fortune-telling is all about, you can look at Four Commandments from Fan, which is a true story of the Ming Dynasty and a family instruction for future generations.

In the eyes of Buddhists, five eyes and six connections are taken for granted, and fortune-telling is just a pediatrics.