Building on the backward Kolmogorov PDE formulated on the Wasserstein space, we establish several new results on the approximation error arising from the Euler–Maruyama discretisation of interacting particle systems associated with McKean-Vlasov diffusions. In particular, we provide explicit error estimates at three levels: trajectory, semigroup (on the Wasserstein space), and density. We further derive Gaussian-type bounds for the transition density of the Euler–Maruyama scheme and for its first-order derivative. This talk is based on two works, the first one with Clément Rey (École Polytechnique) and the other one with Xuanye Song (Université Paris Cité).