Galaxy clusters at low redshift are dominated by massive quiescent galaxies hosting stellar populations 10 Gyrs old, indicating that they were formed in the early universe when clusters were still in the process of being assembled (i.e., protoclusters). The rapid growth of galaxies within protoclusters is driven by the efficient transformation of the cold gas reservoir into stars until the sudden shutting down of star formation. However, the exact mechanisms governing this phase of accelerated galaxy evolution remain unsettled, with both supermassive black hole growth and environmental effects as the main contenders. To shed light on this question, we obtain CO(1-0) molecular gas information with the Australia Telescope Compact Array on a sample of 30 spectroscopically confirmed H emitters in the Spiderweb protocluster at z = 2.16, and Alpha investigate the link between their star formation, AGN activity, and molecular gas reservoirs as a function of environment. We discuss the relative importance of in-/outflow processes in regulating the accelerated evolution of star-forming galaxies at the early phases of cluster assembly and propose a combination of AGN feedback and overconsumption as the main mechanisms leading to the onset of the red sequence in this massive cluster in formation at the cosmic noon.