Kant's modal semantics are rather novel, or he tried to make them out to be so, at any rate (he seems mostly successful, in my opinion; not that his position is confirmed beyond all doubt, but at least he was offering a relatively new idea). In the first Critique, he says at one point:
Possibility, existence, and necessity nobody has ever yet been able to explain without being guilty of manifest tautology, when the definition has been drawn entirely from the pure understanding. For the substitution of the logical possibility of the conception—the condition of which is that it be not self-contradictory, for the transcendental possibility of things—the condition of which is that there be an object corresponding to the conception, is a trick which can only deceive the inexperienced.27
27 In one word, to none of these conceptions belongs a corresponding object, and consequently their real possibility cannot be demonstrated, if we take away sensuous intuition—the only intuition which we possess—and there then remains nothing but the logical possibility, that is, the fact that the conception or thought is possible—which, however, is not the question; what we want to know being, whether it relates to an object and thus possesses any meaning.
For Kant, even necessity "is not a predicate." Ditto for possibility, for he says elsewhere that a hundred possible dollars (thalers) are not qualitatively different from a hundred real dollars.
So when Kant says that his category-based principles are necessary, he is not speaking of the kind of free-floating necessity that theologians attached to God:
Finally, as regards the third postulate, it applies to material necessity in existence, and not to merely formal and logical necessity in the connection of conceptions. Now as we cannot cognize completely a priori the existence of any object of sense, though we can do so comparatively a priori, that is, relatively to some other previously given existence—a cognition, however, which can only be of such an existence as must be contained in the complex of experience, of which the previously given perception is a part—the necessity of existence can never be cognized from conceptions, but always, on the contrary, from its connection with that which is an object of perception. But the only existence cognized, under the condition of other given phenomena, as necessary, is the existence of effects from given causes in conformity with the laws of causality. It is consequently not the necessity of the existence of things (as substances), but the necessity of the state of things that we cognize, and that not immediately, but by means of the existence of other states given in perception, according to empirical laws of causality.
Further reading: "Transcendental Arguments (Stanford Encyclopedia of Philosophy)".