Context. Decades after their discovery, only four hydrogen-deficient carbon (HdC) stars were known to have no circumstellar dust shell. This is in complete contrast to the ∼130 known Galactic HdC stars that are notorious for being heavy dust producers, i.e. the R Coronae Borealis (RCB) stars. Together they form a rare class of supergiant stars that are thought to originate from the merger of CO/He white dwarf (WD) binary systems, otherwise known as the double degenerate scenario. Aims. We searched for new dustless HdC (dLHdC) stars to understand their Galactic distribution, to estimate their total number in the Milky Way and to study their evolutionary link with RCB stars and extreme Helium stars, the final phase of HdC stars. Methods. We used primarily the 2MASS and GAIA eDR3 all-sky catalogues to select candidates that were then followed up spectroscopically. We studied the distribution of known and newly discovered stars in the HR diagram. Results. We discovered 27 new dLHdC stars, one new RCB star, and two new EHe stars. Surprisingly, 20 of the new dLHdC stars share a characteristic of the known dLHdC star HD 148839, having lower atmospheric hydrogen deficiencies. The uncovered population of dLHdC stars exhibit a Bulge-like distribution, like the RCB stars, but show multiple differences from those that indicate they are a different population of HdC stars following its own evolutionary sequence with a fainter luminosity and also a narrow range of effective temperatures, between 5000 and 8000 K. Not all the new dLHdC stars belong to that new population, as we found indication of a current low dust production activity around four of them: the warm F75, F152, C526 and the cold A166. Those could in fact be typical RCB stars passing through a transition time, going in or out of the RCB phase. Conclusions. For the first time we have evidence of a large range of absolute magnitude in the overall population of HdC stars, spanning more than 3 mag. In the favoured formation framework, this is explained by a large range in the initial total WD binary mass which leads to a series of evolutionary sequences with distinct maximum brightness and initial temperature. The cold Galactic RCB stars are also noticeably fainter than the Magellanic ones, possibly due to a difference in metallicity between the original population of stars resulting in different WD mass ratio. The unveiled population of dLHdC stars indicates that the ability to create dust could be linked to the initial total mass. In our Galaxy, there could be as many dLHdC stars as RCB stars.