A law of thin processes with neighbour-count thinning

We consider the superposition $S_n$ of $n$ i.i.d. simple point processes on $\mathbb{R}^d$ and apply a dependent thinning $T_n$, where the retention probability of a point depends on its local neighbour count within a radius $r_n$. While superpositions under independent thinning converge to Poisson