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This paper presents the results of 475 hours of interferometric observationswith the Australia Telescope Compact Array towards the Spiderweb protoclusterat \(z=2.16\). We search for large, extended molecular gas reservoirs among 46previously detected CO(1-0) emitters, employing a customised method wedeveloped. Based on the CO emission images and position-velocity diagrams, aswell as the ranking of sources using a binary weighting of six differentcriteria, we have identified 14 robust and 7 tentative candidates that exhibitlarge extended molecular gas reservoirs. These extended reservoirs are definedas having sizes greater than 40 kpc or super-galactic scale. This resultsuggests a high frequency of extended gas reservoirs, comprising at least \(30\%\) of our CO-selected sample. An environmental study of the candidates iscarried out based on N-th nearest neighbour and we find that the largemolecular gas reservoirs tend to exist in denser regions. The spatialdistribution of our candidates is mainly centred on the core region of theSpiderweb protocluster. The performance and adaptability of our method arediscussed. We found 13 (potentially) extended gas reservoirs located in ninegalaxy (proto)clusters from the literature. We noticed that large extendedmolecular gas reservoirs surrounding (normal) star-forming galaxies inprotoclusters are rare. This may be attributable to the lack of observationslow-J CO transitions and the lack of quantitative analyses of molecular gasmorphologies. The large gas reservoirs in the Spiderweb protocluster are apotential source of the intracluster medium seen in low redshift Virgo- orComa-like galaxy clusters.

COALAS II. Extended molecular gas reservoirs are common in a distant, forming galaxy cluster