Log Manin's conjecture for klt Campana points

Let $(X, D_\epsilon = \sum_{\alpha \in \mathcal A} \epsilon_\alpha D_\alpha)$ be a klt Fano Campana orbifold over a number field $F$, let $L$ be a big $\mathbb Q$-divisor on $X$, and let $a((X,D_\epsilon),L)$ and $b(F,(X,D_\epsilon),L)$ be the associated birational invariants. Let $S$ be a finite set of places containing $\Omega_F^\infty$, let $(\mathcal X,\mathcal D_\epsilon)$ be a regular projective model over $\operatorname{Spec}\mathcal O_{F,S}$, and let $\mathcal L$ be an adelically metrized big and nef $\mathbb Q$-divisor on $X$. Write $N(Q,\mathcal L,T)=\#\{x\in Q\mid \mathsf H_{\mathcal L}(x)\leq T\}$. Log Manin's conjecture. If $(\mathcal X,\mathcal D_\epsilon)(\mathcal O_{F,S})$ is not thin, then there exist a thin set $Z\subset(\mathcal X,\mathcal D_\epsilon)(\mathcal O_{F,S})$ and a constant $c>0$ such that

$$N((\mathcal X,\mathcal D_\epsilon)(\mathcal O_{F,S})\setminus Z,\mathcal L,T)\sim cT^{a((X,D_\epsilon),L)}(\log T)^{b(F,(X,D_\epsilon),L)-1}$$

as $T\to\infty$. This is the proposed asymptotic for counting klt Campana points of bounded height; the source does not state a resolution status, so the conjecture is recorded as open.