  Emergent modified gravity provides a covariant, effective framework for
obtaining spherically symmetric black hole solutions in models of loop quantum
gravity with scale-dependent holonomy modifications. Exact solutions for vacuum
black holes in the presence of a cosmological constant are derived here and
analyzed in four different gauges, explicitly related to one another by
standard coordinate transformations. The global structure is obtained by gluing
space-time regions corresponding to the gauge choices, reconstructing a
non-singular wormhole space-time for an arbitrary scale-dependent holonomy
parameter. This outcome demonstrates the robustness of black-hole models with
covariant holonomy modifications under quantization ambiguities. Compared with
previous constructions, full covariance of the resulting space-time models as
derived here implies subtle new effects and leads to a novel understanding of
the parameters in holonomy modifications, distinguishing a constant holonomy
length from a possibly scale-dependent function that may change coefficients of
holonomy terms. New physical results are obtained for instance in the context
of a non-trivial zero-mass limit of holonomy-modified space-times. The
existence of a consistent effective space-time structure implies various novel
aspects of a net gravitational stress-energy and related thermodynamical
properties.
