  We discuss the entanglement entropy for a massive Klein-Gordon field in two
Schwarzschild-like quantum black hole spacetimes, also including a nonminimal
coupling term with the background scalar curvature. To compute the entanglement
entropy, we start from the standard spherical shell discretisation procedure,
tracing over the degrees of freedom residing inside an imaginary surface. We
estimate the free parameters for such quantum metrics through a simple physical
argument based on Heisenberg uncertainty principle, along with alternative
proposals as asymptotic safety, trace anomaly, and graviton corpuscular
scaling. Our findings reveal a significant decrease in entropy compared to the
area law near the origin for the quantum metrics. In both scenarios, the
entanglement entropy converges to the expected area law sufficiently far from
the origin. We then compare these results to the entropy scaling in regular
Hayward and corrected-Hayward spacetimes to highlight the main differences with
such regular approaches.
