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, that is 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. 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 (EHe) stars, the final phase of HdC stars. We primarily used 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 Hertzsprung-Russell diagram. 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 exhibits a bulge-like distribution, like the RCB stars, but show multiple differences from RCB stars that indicate that they are a different population of HdC stars. This population follows its own evolutionary sequence with a fainter luminosity and also a narrow range of effective temperatures, between 5000 and 8000K. Not all the new dLHdC stars belong to this new population, as we found an indication of a current low dust production activity around 4 of them: the warm F75, F152, and C526, and the cold A166. They might be typical RCB stars passing through a transition time, entering or leaving the RCB phase. For the first time, we have evidence of a wide range of absolute magnitudes in the overall population of HdC stars, spanning more than 3mag. In the favoured formation framework, this is explained by a wide 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 RCB stars, possibly due to a difference in metallicity between the original population of stars, resulting in a different WD mass ratio. The unveiled population of dLHdC stars indicates that the ability to create dust might be linked to the initial total mass. In our Galaxy, there could be as many dLHdC stars as RCB stars.