This work introduces a new mathematical framework based on variable-order post-quantum calculus defined over an arbitrary non-commutative time-scale manifold. Standard quantum calculus, $q$-calculus, and its two-parameter extension $(p,q)$-calculus inherently break the classical Leibniz rule, rendering standard conservation laws invalid. This paper resolves the resulting conservation crisis by constructing a Generalized Non-Commutative Covariant Differential Geometry governed by dynamically shifting parameters $p(t)$ and $q(t)$. We prove the existence and uniqueness of these variable-order dynamic maps using fixed-point topology, establish the nilpotency of the exterior derivative operator via a braided twist operator, and derive a closed-form expression for the Modified Noether Identity. This framework demonstrate that the apparent violation of energy-momentum conservation is clearly balanced by a geometric, manifold flux tensor $K^µ$, offering a novel alternative to dark energy cosmic dynamics.