Private supervision

Spiritual laws of nature but not contrary to the laws of nature. That is, where luck comes into the picture.

There is no such situation because there is no luck within the laws of nature. I have written here more than once about the absence of gaps in the laws of nature, because they are deterministic.

Once everything is predictable, it is possible to plan everything, starting with the laws of nature and with the choices that each person has (meaning the paths are predictable, but it is not known which path will happen according to each person's choice).

That's absolutely true. But it has nothing to do with the question of divine intervention and deviations from the laws of nature. The laws of nature are the plan for what will happen with every choice I make.

That's what I meant. But what's hard for me is that if that's the case, then what's the point of saying there's providence at all? What does providence mean? And what's the difference between private providence and general providence?

In my opinion, there is no providence in the sense of divine involvement in the world. What I called active providence. It is possible that in rare cases this happens (it cannot be ruled out). The matter has been detailed and discussed at length here on the site.