I am not a student of Kant, and i have not studied him. So i can’t say much about his questions of predicates.
But If i see an apple, i don’t just see a nature, i also see a nature that exists; it is the difference between something potentially real and actually real. This could mean only two things. The apples nature is identical with its existence, it exists because it is an apple, because that’s what it is to be an apple, to exist as one. This is clearly not the case since we see apples begin to be apples and thus the act of existing cannot be reduced to the intrinsic nature of the apple, so something more is happening to the apple than simply it’s nature.
The only other possibility is that existence is something given. The apple was only potential and then that potential was actualized by something that was already actual, or existing. If the apple has been given existence then that would mean that the act of existing is not intrinsic to the apples nature and thus there is necessarily a distinction between the nature of the apple and the act of its existing even when it exists. In other-words Its nature is to be an apple, but it’s nature cannot be consider as that which exists because it is an apple. So the concept of existence cannot simply be the nature of the apple. Existence must be something more than that.
So we cannot think of existence as merely a predicate or as something that is merely descriptive of what a potential nature is once it is actual. Every time a thing begins to exist there is a relationship at work.
This distinction between a things nature and its act of existing cannot regress infinitely. You will have to posit a nature that is existence, a being whose nature is to exist in order to explain why a potential or possible being can become actual and remain actual at any point. Thus it is correct to say that God is existence.
This is all logically necessary. So if Kant is saying that existence is not a nature, he is wrong. Existence is a nature, and that nature makes other natures exist. These natures that begin to exist, exist only analogously in the respect that they are being caused to exist and are being sustained in existence rather than existence being something that they are by nature. They have there own act, but that act is their nature alone and is not that by which they exist. Their nature is being made real by God.