We study the intrinsic large-scale distribution and evolution of seven highly ionized metals in the IllustrisTNG magneto-hydrodynamical cosmological simulation. We focus on the fractions of CII, CIV, MgII, NV, NeVIII, OVI, and SiIV in different cosmic web structures (filaments, haloes, and voids) and gas phases (warm-hot intergalactic medium WHIM, hot, diffuse, and condensed gas) from $z=6$ to $z=0$. Our analysis provides a new perspective to the understanding of the distribution and evolution of baryons across cosmic time and, in turn, gives new hints in the context of the well known missing baryons problem. In this work, the cosmic web components are identified using the local comoving dark matter density, which represents a simple and unique way of mapping baryons on large scales. Our results show that MgII and CII are mostly located in condensed gas in haloes in high-density, low-temperature, star-forming regions. The mass fractions of CIV and SiIV, on the other hand, show similar evolutionary trends in the different gas phases and cosmic web environments. Finally, our findings confirm the notion that OVI, NeVIII, and NV exist mainly in the form of diffuse and WHIM gas located in filaments, suggesting that these ionized metals are good tracers of warm/hot and low-density gas, regions that are likely to contain most of the missing baryons in the local Universe.