PSTV-A conjecture for Campana points on Fano orbifolds

Let $(X,D)$ be a klt Campana orbifold over $K$ with a good integral model $(\mathcal{X},\mathcal{D})$ over $\mathcal{O}_{K,S}$. Let $H_{\mathcal{L}}$ be the height associated with an adelically metrized big and nef line bundle, and let $a$ and $b$ be defined by

$$a=\inf\{t\in\mathbb{R}:t[L]+[K_X]+[D]\in\Lambda_{\operatorname{eff}}\},$$

where $b$ is the codimension of the minimal supported face of $\Lambda_{\operatorname{eff}}$ containing $a[L]+[K_X]+[D]$. Assume that $-(K_X+D)$ is ample, so that the orbifold is Fano, and that the set of Campana points $(\mathcal{X},\mathcal{D})(\mathcal{O}_{K,S})$ is not thin. PSTV-A conjecture. There exists a thin set $\mathcal{T}$ of Campana $\mathcal{O}_{K,S}$-points such that

$$\#\{P\in(\mathcal{X},\mathcal{D})(\mathcal{O}_{K,S})\setminus\mathcal{T}:H_{\mathcal{L}}(P)\leqslant B\}\sim c_{\textrm{PSTV-A}}B^a(\log B)^{b-1}$$

as $B\to\infty$, where $c_{\textrm{PSTV-A}}>0$ is an explicit constant.