  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 [CI], CO(1-0) and CO(4-3) performed with the Atacama Large
Millimeter Array (ALMA) and Australia Telescope Compact Array (ATCA). [CI] 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 MRC1138-262 shows a very high global $L'_{\rm CO(4-3)}$/$L'_{\rm
CO(1-0)}$ ~ 1, suggesting that mechanisms other than FUV-heating by star
formation prevail at the heart of the Spiderweb Galaxy. Contrary, the CGM has
$L'_{\rm CO(4-3)}$/$L'_{\rm CO(1-0)}$ and $L'_{\rm [CI]}$/$L'_{\rm CO(1-0)}$
similar to the ISM of five galaxies in the wider proto-cluster, and its carbon
abundance, $X_{\rm [CI]}$/$X_{\rm H2}$, resembles that of the Milky Way and
starforming 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 GCM.
