purpose of 'existence — Jack Cummins

How do you know existence has "purpose"? What is that "purpose"?

a person's construction of 'reality

If "a person" is real, then s/he belongs to "reality", therefore s/he cannot "construct reality".

'beyond' the physical

By "beyond" you mean like math or poetry?

The existence of noumena has not been asserted or denied anywhere in the work. To call it a realm is to ignore:

The concept of a noumenon is therefore merely a boundary concept, in order to limit the pretension of sensibility, and therefore only of negative use. But it is nevertheless not invented arbitrarily, but is rather connected with the limitation of sensibility, yet without being able to posit anything positive outside of the domain of the latter.
— ibid. A255/B311

I am not aware of any place in the Critique where Kant argued differently from this. — Paine

I have already told you I believe CPR is inconsistent. So I'm not surprised Kant makes contradictory claims. The best we can do is give his intended & inconsistent reading.

Going back to a very old objection. For Kant, the transcendental object is the CAUSE of all appearances & clearly not an appearance. The obvious problem here is there is no sense in attributing a causal or grounding role to that which you don't even know if it exists or not. The agnosticism must apply to its causal & grounding role as well.

You may retort that the transcendental object is more like a rule or procedure but this makes no sense. It does not belong to any category of Kant, nor do the categories have anything to do with it, except maybe for causation (in contradiction)

But the understanding thinks it only as transcendental object. This object is the cause of appearance (hence is not itself appearance) and can be thought neither as magnitude nor as reality nor as substance, etc. (because these concepts always require sensible forms wherein they determine an object). Hence concerning this object we are completely ignorant as to whether it is to be found in us--or, for that matter, outside us; and whether it would be annulled simultaneously with sensibility, or would still remain if we removed sensibility. If we want to call this object noumenon, because the presentation of it is not sensible, then we are free to do so. — CPR, A288,B344,Pluhar

So yes. CPR is irredeemable. It's full of contradictions. Kant to me is simply a dumber version of Sextus Empiricus, who was smart enough to use noumena & phenomena as dispensable distinctions, ready to be thrown out in the manner of Wittgenstein's (who was also a Pyrrhonist) ladder once the job has been accomplished.