Resonant inelastic x-ray scattering (RIXS) is an evolving tool for investigating the spin dynamics of strongly correlated materials, which complements inelastic neutron scattering. In isotropic spin-1/2 Heisenberg antiferromagnetic (HAFM) spin chains, both techniques have observed non-spin-conserving (NSC) excitations confined to the two-spinon phase space. However, a recent O K-edge RIXS study of the one-dimensional HAFM Sr₂CuO₃ observed spin-conserving (SC) four-spinon excitations outside the two-spinon phase space. Here, we demonstrate that analogous four-spinon excitations can also be accessed at the Cu L₃ edge in the related material SrCuO₂. Through detailed modeling, we establish that these excitations appear in both the SC and NSC channels of the Cu L₃ edge, and are only captured by higher-order terms in the ultrashort core-hole lifetime expansion. Since these terms encode information about spin-spin correlations extending beyond nearest neighbors, our results offer different possibilities for studying nonlocal spin correlations in quantum magnets.