In all religions what ever existed there are soul and God
Hinduism doesn't have 'God'; it does have Brahman, which is sometimes identified with it; since in this sense it is a monotheistic aspect of Hinduism, as for example exemplified in the Upanishads; but this doesn't mean the same thing. For example the Catholic doctrine of the Trinity as a description of God is not found in Hinduism.
Nor is the Hindu concept of soul atma similar; in Advaita Vedanta (non-dualism), an Indian philosophical school, the atma is identical with Brahman; in Dvaita Vedanta distinguishes, at least partly between the two.
Still, in a broad sense you are right; one can distinguish notions in most religions that correspond in some sense with the distinction that you make.
From physics we know that there is no difference between particle without eletrical charge, gravity, mass and energy and non-existing particle - both of them can affect the universe as well - they can not.
Sure: In the physical sciences; one aspect of truth( and a large part of it) is instrumental; we know a particle exists when it has an effect; and by depriving them of charges - electric or gravitational; so that they do not interact with anything; it can't be distinguished from a particle that is not there at all.
What you receive better: a universe in which God has no ability to affect anything or universe in which anything does not make sense, because something without any physical properties can not influence anything.
This appears to be a personal declaration disguised as a rhetorical question
How can interact res cogitans and res extensa?
There are quite a number of different theories. Descarte wrote in Passions of the Soul, his last book that:
We need to recognize that the soul is really joined to the whole body, and that we cannot properly say that it exists in any one part of the body to the exclusion of the others.
For the body is a unity which is in a sense indivisible because of the arrangement of its organs, these being so related to one another that the removal of any one of them renders the whole body defective.
And the soul is of such a nature that it has no relation to extension, or to the dimensions or other properties of the matter of which the body is composed: it is related solely to the whole assemblage of the body's organs.
This is obvious from our inability to conceive of a half or a third of a soul, or of the extension which a soul occupies. Nor does the soul become any smaller if we cut off some part of the body, but it becomes completely separate from the body when we break up the assemblage of the body's organs”
This conclusion (if not the argument) was already in St Augustine, in his book On the Trinity:
In each body the whole soul is in the whole body, and whole in each part of it
For Descarte the soul is not the principle of life; but the principle of thought. Taking into all his other account, at least twelve other different accounts of his solution to the mind-body problem has been put forward.