Using the IllustrisTNG and TNG-Cluster simulations, I quantify the impact of satellite galaxies on the CGM as functions of satellite stellar mass, host halo mass, and cosmic time. Before infall, satellite galaxies were still central galaxies with their own multiphase CGM and ISM, undergoing feedback from star-formation and/or SMBHs. As they fall into other larger hosts, ranging from MW-like galaxies to the largest clusters in the Universe, both their CGM and ISM are redistributed due to both internal feedback processes and external environmental effects, such as ram pressure stripping. Namely, satellites deposit their own gaseous reservoirs into the host halos, contributing to both the cool and hot gas in the CGM. In particular, I follow the evolution of ~500 jellyfish galaxies in TNG50 as they deposit their cool, metal-enriched ISM into their host halos. Meanwhile, some massive cluster satellites in TNG-Cluster are able to retain their own CGM, contributing to the overall soft X-ray flux in the intracluster medium (ICM). Further, I show that the ICM today is multiphase, where clusters tend to have ~10^9-10 Msun of cool gas in their halos, according to TNG-Cluster. In the past, however, these cluster progenitors had ~10^12-12 Msun of gas, orders of magnitude more than today. The evolution of the cool ICM since z <~ 4, which holds for lower mass halos as well, is a complex interplay between new cool gas sources and sinks, including accretion from large scale filaments, satellite stripping, gas cooling, and gas heating via AGN feedback and virial shocks. Lastly, I discuss in-situ ICM star-formation and potential Halpha emission therefrom, and compare the MgII column density profiles in TNG-Cluster to recent SDSS stacks, where TNG-Cluster naturally produces a signficant amount of MgII absorbers.