existentialism

In the book “True and Unstable” you argued that relying on intuition is an essential part of learning about the world.. Don't existential experiences fall into this category? (It seems to me that such experiences can be trusted, especially when many people have the same experience)

I don't call that existentialism. Every philosophical discipline starts with initial intuitions from which the axioms are created. Existentialism is closer to experiences and psychology.

I still can't understand the difference... in the context of faith, for example: If a person experiences the world directly, let's say, and thus assumes that such and such an external world exists - and then through a logical process he deduces from the existence of this world the existence of God, why is his philosophical process more reliable than a person who experiences God himself directly? (And from this experience he can conclude, for example, that God exists, that He demands something of Him, or that He loves Him, depending on the nature of the experience)

There is no difference. The question is whether it is an experience or a recognition. If it is an experience, it is existentialism and it has no meaning on the factual level. If it is a recognition or an intuitive insight, then it is not existentialism, and in both cases it is perfectly fine.

So if I understand correctly, I can divide existential thought between descriptions of experiences and descriptions of “cognitions”:
That is, if the thinker describes an experience of loneliness or an experience of absurdity, for example, this has nothing to do with philosophy because philosophy by definition deals with the world outside of man and not with man himself(?). Such experiences are more related to the field of psychology.
On the other hand, if the thinker describes something like his experience with things outside of him - like God, he can deduce from this insights about God (say - that God is greater than him or that He demands something from him) and then the thinker and those who identify with his feelings will be able to treat this information as valid on the factual level because they arrived at it in the form of recognition of the world (which is what is called philosophy)

But even from the analysis of the first type (the person's experiences) conclusions can be drawn about the person himself and perhaps also about the world, right? (If a person feels a moral obligation, which is what existentialism deals with, he can develop philosophical conclusions about good and evil or the existence of commanding authority)

Precise. In my book True and Unstable (see a bit in the fourth notebook here) I explained that “feeling” a moral obligation means recognition, not experience.

Sorry for the digging, but now I'm a little confused... At first you said that existentialism is generally devoid of philosophical value, but at the end you said that the "knowledge" that existentialist thinkers describe can lead to philosophical conclusions on the factual level, and that sometimes the experiences described are actually knowledge, as in the case of ethical feelings.

I will explain once again because we have already exhausted ourselves. When there are basic insights that are based on intuition, philosophical conclusions can be drawn from them. This is not existentialism, since all philosophy is structured this way. But experiences that lead to psychological insights are not philosophy.