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This paper is the second of a series that tackles the properties of molecular gas in galaxies residing in clusters and their related large-scale structures. Out of 21 targeted fields, 19 galaxies were detected in CO(3-2) with the Atacama Large Millimeter Array (ALMA), including two detections within a single field. These galaxies are either bona fide members of the CL1301.7$-$1139 cluster ($z=0.4828$, $\sigma_{cl}=681$ km s$^{-1}$), or located within $\sim 7 \times R_{200}$, its virial radius. They have been selected to sample the range of photometric local densities around CL1301.7$-$1139, with stellar masses above log($M_{\rm star}$) = 10, and to be located in the blue clump of star-forming galaxies derived from the $u$, $g$, and $i$ photometric bands. Unlike previous works, our sample selection does not impose a minimum star formation rate or detection in the far-infrared. As such and as much as possible, it delivers an unbiased view of the gas content of normal star-forming galaxies at $z \sim 0.5$. Our study highlights the variety of paths to star formation quenching, and most likely the variety of physical properties (i.e. temperature, density) of the corresponding galaxy's cold molecular gas. Just as in the case of CL1411.1$-$1148, although to a smaller extent, we identify a number of galaxies with lower gas fraction than classically found in other surveys. These galaxies can still be on the star-forming main sequence. When these galaxies are not inside the cluster virialised region, we provide hints that they are linked to their infall regions within $\sim 4 \times R_{200}$., Comment: 15 pages, 11 figures, accepted for publication in A&A. arXiv admin note: text overlap with arXiv:2012.09592