Context.Jets are rarely associated with pre-main sequence intermediate-mass stars. This contrasts with the frequent detection of jets in lower mass or younger stars. Optical and near-IR observations of jet-driving sources are often hindered by the presence of a natal envelope.Aims.Jets around partly embedded sources are a useful diagnostic to constrain the geometry of the concealed protoplanetary disk. We intend to clarify how the jet-driving mechanisms are affected by both spatial anisotropies and episodic variations at the (sub-)au scale from the star.Methods.We obtained a rich set of high-contrast VLT/SPHERE observations from 0.6 to 2.2μm of the young intermediate-mass star RY Tau. Given the proximity to the Sun of this source, our images have the highest spatial resolution ever obtained for an atomic jet (down to ~4 au).Results.Optical observations in polarized light show no sign of the protoplanetary disk detected by ALMA. Instead, we observed a diffuse signal resembling a remnant envelope with an outflow cavity. The jet is detected in the Hα, [S II] at 1.03μm, He Iat 1.08μm, and [Fe II] lines in the 1.25μm and 1.64μm. The jet appears to be wiggling and its radial width increasing with the distance is complementary to the shape of the outflow cavity suggesting a strong interaction with jet and envelope. Through the estimated tangential velocity (~100 km s⁻¹), we revealed a possible connection between the launching time of the jet substructures and the stellar activity of RY Tau.Conclusions.RY Tau is at an intermediate stage toward the dispersal of the natal envelope. This source shows episodic increases of mass accretion and ejection similarly to other known intermediate-mass stars. The amount of observed jet wiggle is consistent with the presence of a precessing disk warp or misaligned inner disk that would be induced by an unseen planetary or sub-stellar companion at sub- or few-au scales respectively. The high disk mass of RY Tau and of two other jet-driving intermediate-mass stars, HD 163296 and MWC480, suggests that massive, full disks are more efficient at launching prominent jets.