Understanding how turbulent energy cascades across spatial scales and thermal phases is key to deciphering the physics that governs cosmic gas dynamics. Recent observations reveal that turbulent energy transfer rates remain remarkably constant in dense molecular clouds over vastly different scales in the Milky Way. Similar rates are also found in the large-scale diffuse environment of supermassive black holes at high redshifts. This similarity is all the more puzzling since the feedback energy release of supermassive black holes is colossal compared to that of stellar-driven feedback. The UChicago-ENS-Paris team leverages the complementary expertise of observers in the former and numericists and theorists in the latter to investigate how feedback energy from star formation and supermassive black holes cascades in their large-scale environment, bridging interstellar and circumgalactic studies across cosmic time.