Context . The (sub-)millimetre dust opacity spectral index ( β ) is a critical observable for constraining dust properties, such as the maximum grain size of an observed dust population. It has been widely measured at Galactic scales and down to protoplanetary disks. Because of observational and analytical challenges, however, quite a gap exists in following the evolution of dust in the interstellar medium (ISM): we lack measures of the dust properties in the envelopes that feed newborn protostars and their disks.…