We perform a systematic ab initio study of the electronic structure of Sr(V,Mo,Mn)O3 perovskites, using the parameter-free GW+EDMFT method. This approach self-consistently calculates effective interaction parameters, taking into account screening effects due to nonlocal charge fluctuations. Comparing the results of a 3-band (t2g) description to those of a 5-band (t2g+eg) model, it is shown that the eg states have little effect on the low-energy properties and the plasmonic features for the first two compounds but play a more active role in SrMnO3. In the case of SrMnO3 paramagnetic GW+EDMFT yields a metallic low-temperature solution on the verge of a Mott transition, while antiferromagnetic GW+EDMFT produces an insulating solution with the correct gap size. We discuss the possible implications of this result for the nature of the insulating state above the Neel temperature, and the reliability of the GW+EDMFT scheme.