Existence of rigid symmetric monoidal categorifications of algebraic closures of finite fields

Let $p$ be a prime. A rigid symmetric monoidal $b\mathbb{Z}d$-linear category is a rigid symmetric monoidal category enriched over $b\mathbb{Z}d$-modules; write $K_0(C)$ for its Grothendieck ring, and let $b\overline{\mathbb{F}}_pd$ denote the algebraic closure of the finite field with $p$ elements. Existence conjecture. For each prime $p$, there exists a rigid symmetric monoidal $b\mathbb{Z}d$-linear category $C$ such that

$$K_0(C) \cong \overline{\mathbb{F}}_p.$$

A positive solution would remove the characteristic-zero assumption on the minimal primes in the functorial categorification result and extend its method to the corresponding positive-characteristic case. The supplied context does not state whether this conjecture has been resolved.