The circumgalactic medium (CGM) of the massive Spiderweb Galaxy, a conglomerate of merging proto-cluster galaxies at z = 2.2, forms an enriched interface where feedback and recycling act on accreted gas. This is shown by observations of [C I], CO(1-0), and CO(4-3) performed with the Atacama Large Millimeter Array and Australia Telescope Compact Array. [C I] and CO(4-3) are detected across ˜50 kpc, following the distribution of previously detected low-surface-brightness CO(1-0) across the CGM. This confirms our previous results on the presence of a cold molecular halo. The central radio galaxy MRC 1138-262 shows a very high global L^'_CO(4-3)/L^'_CO(1-0) ˜ 1, suggesting that mechanisms other than FUV-heating by star formation prevail at the heart of the Spiderweb Galaxy. Contrary, the CGM has L^'_CO(4-3)/L^'_CO(1-0) and L^'_[C I]/L^'_CO(1-0) similar to the ISM of five galaxies in the wider proto-cluster, and its carbon abundance, X_[C I]/X_H_2, resembles that of the Milky Way and star-forming galaxies. The molecular CGM is thus metal-rich and not diffuse, confirming a link between the cold gas and in situ star formation. Thus, the Spiderweb Galaxy grows not directly through accretion of gas from the cosmic web, but from recycled gas in the CGM.