A search is presented for hadronic signatures of beyond the Standard Model (BSM) physics, with an emphasis on signatures of a strongly coupled hidden dark sector accessed via resonant production of a Z′ mediator. The ATLAS experiment dataset collected at the Large Hadron Collider from 2015 to 2018 is used, consisting of proton-proton collisions at s=13  TeV and corresponding to an integrated luminosity of 140  fb-1. The Z′ mediator is considered to decay to two dark quarks, which each hadronize and decay to showers containing both dark and Standard Model particles, producing a topology of interacting and noninteracting particles within a jet known as “semivisible.” Machine learning methods are used to select these dark showers and reject the dominant background of mismeasured multijet events, including an anomaly detection approach to preserve broad sensitivity to a variety of BSM topologies. A resonance search is performed by fitting the transverse mass spectrum based on a functional form background estimation. No significant excess over the expected background is observed. Results are presented as limits on the production cross section of semivisible jet signals, parametrized by the fraction of invisible particles in the decay and the Z′ mass, and by quantifying the significance of any generic Gaussian-shaped mass peak in the anomaly region.