Not yet reviewed by Pith; the record is open.

We build upon the state-of-the-art semi-analytic model \texttt{FEGA24} (Formation and Evolution of GAlaxies, \citealt{contini2024d}), which integrates the latest prescriptions relevant to galaxy formation and evolution, alongside a comprehensive AGN feedback model. This model incorporates three modes of feedback: negative (preventing excessive cooling), positive (enhancing star formation), and hot gas ejection (expelling gas beyond the virial radius of halos). These modes operate in a coordinated manner: the negative mode regulates the cooling process, the positive mode promotes bursts of star formation, and the hot gas ejection mode expels gas beyond the virial radius when the AGN is sufficiently powerful. Our updated semi-analytic model, \texttt{FEGA25}, retains the qualitative and quantitative consistency of the analyses presented in \cite{contini2024d}, while delivering more robust results. Notably, \texttt{FEGA25} provides a more detailed characterization of the fraction of passive galaxies as a function of stellar mass and redshift, predicts a main sequence of star-forming galaxies more consistent with observations and a more accurate cosmic star formation rate density with redshift. Moreover, it estimates the fraction of hot gas in halos closer to observed values. These findings underscore the importance of a physical mechanism capable of ejecting hot gas beyond the virialized region of dark matter halos without significantly altering the stellar and cold gas components. Such a mechanism is crucial to ensure the proper functioning of other processes, such as cooling and star formation. Since supernova feedback is already modeled at its maximum efficiency, AGN feedback emerges as the natural candidate for this role.