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We study the salt-dependent self-assembly of polyampholytes (PAs) using coarse-grained molecular dynamics simulations with explicit mobile salt ions, supported by theoretical analysis within the random phase approximation (RPA). The sensitivity of aggregation to salt is found to be sequence dependent, in line with the salt sensitivity of the mesophase instability predicted by RPA. For PA chains with distinct charge sequences, we quantify salt-induced changes in aggregation, single-chain dimensions, and structural correlations. Blocky sequences exhibit pronounced, weakly non-monotonic salt responses, with aggregation enhanced at intermediate screening and weakened at higher salt, whereas well-mixed sequences display much weaker and nearly monotonic behavior. In both cases, at sufficiently high salt concentration, the sequence dependence diminishes and the system ultimately collapses into a single large aggregate. We further present the salt dependence of aggregate size distributions, real-space correlation functions, and partial structure factors, the latter evaluated over the restricted wave vector range accessible within the finite simulation box. Charge-charge structure factors reveal enhanced long-wavelength charge fluctuations with increasing salt, consistent with the observed aggregation trends. Within the RPA framework, salt shifts the spinodal lines toward smaller hydrophobicity and reduces the characteristic wave vector of the microphase instability, in correspondence with simulation results. A brief comparison with the highly charged intrinsically disordered protein ProTα underscores the role of a large net charge on salt-induced aggregation.