This paper presents results of searches for the electroweak production of supersymmetric particles in models with compressed mass spectra. The searches use 139 fb(-1) of root s = 13 TeV proton-proton collision data collected by the ATLAS experiment at the Large Hadron Collider. Events with missing transverse momentum and two same-flavor, oppositely charged, low-transverse-momentum leptons are selected, and are further categorized by the presence of hadronic activity from initial-state radiation or a topology compatible with vector-boson fusion processes. The data are found to be consistent with predictions from the Standard Model. The results are interpreted using simplified models of R-parity-conserving supersymmetry in which the lightest ...