Is our existence furnished by divinity? If this means that God causes individual acts of existence, yes, of course. Essence is the limiting factor of a way of existing. So whatever else exists truly does exist, but it is not a constituent of the Unconditioned Reality itself, since it (God) remains distinct as pure existence. If God were existence + a limiting essence, God wouldn’t be the First Unconditioned Cause/Reality after all, and we’d just have to push back ultimate explanation of Reality back one level.
We can’t say that the “stuff” of our being, as individual beings or “substances” (a cat, a human, a water molecule, etc.), is the “stuff” of God in the sense that other beings are just part of God. They are distinct acts of existence caused by God.
Interesting/FYI/P.S.: There is a tension, a balance, that must be maintained. Saying all this means we cannot say that God + the world is more than God. How does this not lead to pantheism? I think imagination is the problem, because we are tempted to conceptualize God as just “another being” (and so limited) along side other beings, even when we know better not to do. But if God is Pure Existence, Pure Act, the Unconditioned Reality, then all things are ultimately “in” Him in the sense that all actual realities can only receive their actualization (becoming this or that; change in general) from pure actuality itself. If not — if say the Cat were not in God in some way — then where would the cat ultimately get its existence?
This actually leads to strong reason to consider God, the First Cause, as most resembling what we consider a Mind. For a cat does not exist in God as physical cat, which is limited. But if not, then it must be in God in some other way — and the only way the form of a cat can be in something (so a Thomist would say) besides in-forming matter (this or that particular cat) would be in a mind, as a concept. There is more to the argument than this, but it’s just a hint that everything so far seems to more and more align with the God of classical theism/traditional Christianity.
And so pantheism is nearing the truth, but it doesn’t get the answer quite right. But even from all that was said above, we still must consider all other beings as reflections of God. All things are “images of God.” This is simply due to the fact that all other beings reflect God, Unconditioned Existence, in various degrees of being. In fact, traditional Thomism would speak of a “hierarchy of being.” Think of God as light, and all other beings as various colors in the spectrum (when the light passes through a prism). But in this example, don’t think of a particular color as part of light, though, but rather as a limited manifestation of the “pure” act of light itself.