We present a population of 20 radio-luminous supernovae (SNe) with emission reaching $L_{ u}{sim}10^{26}-10^{29}rm{erg s^{-1} Hz^{-1}}$ in the first epoch of the Very Large Array Sky Survey (VLASS) at $2-4$ GHz. Our sample includes one long Gamma-Ray Burst, SN 2017iuk/GRB171205A, and 19 core-collapse SNe detected at $approx (1-60)$ years after explosion. No thermonuclear explosion shows evidence for bright radio emission, and hydrogen-poor progenitors dominate the sub-sample of core-collapse events with spectroscopic classification at the time of explosion (73%). We interpret these findings into the context of the expected radio emission from the forward shock interaction with the circumstellar medium (CSM). We conclude that these observations require a departure from the single wind-like density profile (i.e., $rho_{rm{CSM}}propto r^{-2}$) that is expected around massive stars and/or a departure from a spherical Newtonian shock. Viable alternatives include the shock interaction with a detached, dense shell of CSM formed by a large effective progenitor mass-loss rate $dot M sim (10^{-4}-10^{-1})$ M$_{odot}$ yr$^{-1}$ (for an assumed wind velocity of $1000,rm{km,s^{-1}}$); emission from an off-axis relativistic jet entering our line of sight; or the emergence of emission from a newly-born pulsar-wind nebula. The relativistic SN,2012ap that is detected 5.7 and 8.5 years after explosion with $L_{ u}{sim}10^{28}$ erg s$^{-1}$ Hz$^{-1}$ might constitute the first detections of an off-axis jet+cocoon system in a massive star. Future multi-wavelength observations will distinguish among these scenarios. Our VLASS source catalogs, which were used to perform the VLASS cross matching, are publicly available at https://doi.org/10.5281/zenodo.4895112.