A search for cascade decays of charged sleptons and sneutrinos using final states characterized by three leptons (electrons or muons) and missing transverse momentum is presented. The analysis is based on a dataset with 140  fb-1 of proton-proton (pp) collisions at a center-of-mass energy of s=13  TeV recorded by the ATLAS detector at the Large Hadron Collider. This paper focuses on a supersymmetric scenario that is motivated by the muon anomalous magnetic moment observation, dark-mattter relic density abundance, and electroweak naturalness. A mass spectrum involving light Higgsinos and heavier sleptons with a bino at intermediate mass is targeted. No significant deviation from the Standard Model expectation is observed. This search enables us to place stringent constraints on this model, excluding at the 95% confidence level charged slepton and sneutrino masses up to 450 GeV when assuming a lightest neutralino mass of 100 GeV and mass-degenerate selectrons, smuons and sneutrinos.