  We improve and extend our study of the complex in-medium heavy quark
potential and its Debye mass $m_D$ in a gluonic medium with a finer scan around
the deconfinement transition and newly generated ensembles closer to the
thermodynamic limit. On the lattices with larger physical volume, Re[V] shows
signs of screening, i.e. a finite $m_D$, only in the deconfined phase,
reminiscent of a genuine phase transition. Consistently Im[V] exhibits nonzero
values also only above $T_C$. We compare the behavior of Re[V] with the color
singlet free-energies that have been used historically to extract the Debye
mass. An effective coupling constant is computed to assess the residual
influence of the confining part of the potential at $T>0$. Our previous finding
of a gradual screening of Re[V] around $T_C$ on finer lattices is critically
reassessed and interpreted to originate from finite volume artifacts that
affect the deployed $\beta=7$, $\xi_b=3.5$ parameter set at $N_s=32$.
