The holographic Einstein–Maxwell-dilaton model is employed to map state-of-the-art lattice QCD thermodynamics data from the temperature (T) axis towards the baryon–chemical potential ((Formula presented.)) axis and aims to gain a warm equation of state (EoS) of deconfined QCD matter which can be supplemented with a cool and confined part suitable for subsequent compact (neutron) star (merger) investigations. The model exhibits a critical end point (CEP) at (Formula presented.) MeV and (Formula presented.) MeV with an emerging first-order phase transition (FOPT) curve which extends to large values of (Formula presented.) without approaching the (Formula presented.) axis. We consider the impact and peculiarities of the related phase structure on the EoS for the employed dilaton potential and dynamical coupling parameterizations. These seem to prevent the design of an overall trustable EoS without recourse to hybrid constructions.