A search for charged-lepton-flavor violating μτqt (q=u, c) interactions is presented, considering both top-quark production and decay. The data analyzed correspond to 140  fb-1 of proton-proton collisions at a center-of-mass energy of s=13  TeV recorded with the ATLAS detector at the Large Hadron Collider. The analysis targets events containing two muons with the same electric charge, a hadronically decaying τ-lepton and at least one jet, with exactly one b-tagged jet, produced by a μτqt interaction. Agreement with the Standard Model expectation within 1.6 standard deviations is observed, and limits are set at the 95% confidence level (CL) on the charged-lepton-flavor violation branching ratio of B(t→μτq)<8.7×10-7. An effective field theory interpretation is performed yielding 95% CL limits on Wilson coefficients, dependent on the flavor of the associated light quark and the Lorentz structure of the coupling. These range from |clequ3(2313)|/Λ2<0.10  TeV-2 for μτut to |clequ1(2323)|/Λ2<1.8  TeV-2 for μτct. An additional interpretation is performed for scalar leptoquark production inducing charged-lepton-flavor violation, with fixed intergenerational couplings. Upper limits on leptoquark coupling strengths are set at the 95% CL, ranging from λLQ=1.3 to λLQ=3.7 for leptoquark masses between 0.5 and 2.0 TeV.