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

Complex heavy-quark potential and Debye mass in a gluonic medium from lattice QCD