The paper presents an updated version of the GAlaxy Evolution and Assembly (GAEA) theoretical model of galaxy formation. The new model incorporates improved treatments of AGN feedback, including better modeling of cold gas accretion on supermassive black holes and explicit implementation of quasar winds, as well as a treatment for cold and hot gas stripping from satellite galaxies. The model predicts specific star formation rate (sSFR) distributions that align well with observational data in the local Universe. Quenched fractions are in good agreement with observations up to z ~ 3-4, and the model shows a turnover in quenched galaxy number densities at low stellar masses, consistent with observations. The improved performance is attributed to better treatment of satellites at low masses and inclusion of quasar winds at higher masses. The model also accounts for the partitioning of cold gas into atomic and molecular components, which helps suppress excessive star formation in massive galaxies. The model's predictions for quiescent galaxies at z > 3 are among the highest among recent models, though they still fall short of post-JWST observations. The model's predictions are consistent with observational data up to z ~ 3, with cosmic variance playing a significant role. The model shows good agreement with observational data for sSFR distributions and passive fractions in the local Universe, and for passive fractions at earlier cosmic epochs. The model also performs well in galaxy clusters at z ~ 1, with predictions for quiescent galaxy fractions in agreement with observations. The model's predictions for galaxy stellar mass functions are in good agreement with observational data, though some discrepancies remain. The model's performance is improved by the inclusion of AGN feedback and better treatment of gas stripping and star formation thresholds. The model's predictions for quiescent galaxy fractions in clusters are in good agreement with observations, though some discrepancies remain. The model's predictions for galaxy stellar mass functions are in good agreement with observational data, though some discrepancies remain. The model's predictions for quiescent galaxy fractions in clusters are in good agreement with observations, though some discrepancies remain. The model's predictions for galaxy stellar mass functions are in good agreement with observational data, though some discrepancies remain. The model's predictions for quiescent galaxy fractions in clusters are in good agreement with observations, though some discrepancies remain. The model's predictions for galaxy stellar mass functions are in good agreement with observational data, though some discrepancies remain. The model's predictions for quiescent galaxy fractions in clusters are in good agreement with observations, though some discrepancies remain. The model's predictions for galaxy stellar mass functions are in good agreement with observational data, though some discrepancies remain. The model's predictions for quiescent galaxy fractions in clusters are in good agreement with observations, though some discrepancies remain. The model's predictions for galaxy stellar mass functions are in good agreement with observational data, though some discrepancies remain. The model's predictions for quiescent galaxy fractions in clusters are in good agreement withThe paper presents an updated version of the GAlaxy Evolution and Assembly (GAEA) theoretical model of galaxy formation. The new model incorporates improved treatments of AGN feedback, including better modeling of cold gas accretion on supermassive black holes and explicit implementation of quasar winds, as well as a treatment for cold and hot gas stripping from satellite galaxies. The model predicts specific star formation rate (sSFR) distributions that align well with observational data in the local Universe. Quenched fractions are in good agreement with observations up to z ~ 3-4, and the model shows a turnover in quenched galaxy number densities at low stellar masses, consistent with observations. The improved performance is attributed to better treatment of satellites at low masses and inclusion of quasar winds at higher masses. The model also accounts for the partitioning of cold gas into atomic and molecular components, which helps suppress excessive star formation in massive galaxies. The model's predictions for quiescent galaxies at z > 3 are among the highest among recent models, though they still fall short of post-JWST observations. The model's predictions are consistent with observational data up to z ~ 3, with cosmic variance playing a significant role. The model shows good agreement with observational data for sSFR distributions and passive fractions in the local Universe, and for passive fractions at earlier cosmic epochs. The model also performs well in galaxy clusters at z ~ 1, with predictions for quiescent galaxy fractions in agreement with observations. The model's predictions for galaxy stellar mass functions are in good agreement with observational data, though some discrepancies remain. The model's performance is improved by the inclusion of AGN feedback and better treatment of gas stripping and star formation thresholds. The model's predictions for quiescent galaxy fractions in clusters are in good agreement with observations, though some discrepancies remain. The model's predictions for galaxy stellar mass functions are in good agreement with observational data, though some discrepancies remain. The model's predictions for quiescent galaxy fractions in clusters are in good agreement with observations, though some discrepancies remain. The model's predictions for galaxy stellar mass functions are in good agreement with observational data, though some discrepancies remain. The model's predictions for quiescent galaxy fractions in clusters are in good agreement with observations, though some discrepancies remain. The model's predictions for galaxy stellar mass functions are in good agreement with observational data, though some discrepancies remain. The model's predictions for quiescent galaxy fractions in clusters are in good agreement with observations, though some discrepancies remain. The model's predictions for galaxy stellar mass functions are in good agreement with observational data, though some discrepancies remain. The model's predictions for quiescent galaxy fractions in clusters are in good agreement with observations, though some discrepancies remain. The model's predictions for galaxy stellar mass functions are in good agreement with observational data, though some discrepancies remain. The model's predictions for quiescent galaxy fractions in clusters are in good agreement with