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We present the first volume-limited sample of spectroscopically confirmed hot subluminous stars out to 500 pc, defined using the accurate parallax measurements from theGaiaspace mission data release 3 (DR3). The sample comprises a total of 397 members, with 305 (~77%) identified as hot subdwarf stars, including 83 newly discovered systems. Of these, we observe that 178 (~58%) are hydrogen-rich sdBs, 65 are sdOBs (~21%), 32 are sdOs (~11%), and 30 are He-sdO/Bs (~10%). Among them, 48 (~16%) exhibit an infrared excess in their spectral energy distribution fits, suggesting a composite binary system. The hot subdwarf population is estimated to be 90% complete, assuming that most missing systems are these composite binaries located within the main sequence (MS) in theGaiacolour-magnitude diagram. The remaining sources in the sample include cataclysmic variables, blue horizontal branch stars, hot white dwarfs, and MS stars. We derived the mid-plane densityρ₀and scale height h_zfor the non-composite hot subdwarf star population using a hyperbolic sechant profile (sech²). The best-fit values areρ₀= 5.17 ± 0.33 × 10⁻⁷stars pc⁻³and h_z= 281 ± 62 pc. When accounting for the composite-colour hot subdwarfs and their estimated completeness, the mid-plane density increases toρ₀= 6.15_−0.53^+1.16× 10⁻⁷stars pc⁻³. This corrected space density is an order of magnitude lower than predicted by population synthesis studies, supporting previous observational estimates. 

Context. The Transiting Exoplanet Survey Satellite (TESS) mission is revolutionizing the blossoming area of asteroseismology, particularly of pulsating white dwarfs and pre-white dwarfs, thus continuing the impulse of its predecessor, the Kepler mission. Aims. In this paper, we present the observations from the extended TESS mission in both 120 s short-cadence and 20 s ultra-short-cadence mode of two pre-white dwarf stars showing hydrogen deficiency. We identify them as two new GW Vir stars, TIC 333432673 and TIC 095332541. We apply the tools of asteroseismology with the aim of deriving their structural parameters and seismological distances. Methods. We carried out a spectroscopic analysis and a spectral fitting of TIC 333432673 and TIC 095332541. We also processed and analyzed the high-precision TESS photometric light curves of the two target stars, and derived their oscillation frequencies. We performed an asteroseismological analysis of these stars on the basis of PG 1159 evolutionary models that take into account the complete evolution of the progenitor stars. We searched for patterns of uniform period spacings in order to constrain the stellar mass of the stars. We employed the individual observed periods to search for a representative seismological model. Results. The analysis of the TESS light curves of TIC 333432673 and TIC 095332541 reveals the presence of several oscillations with periods ranging from 350 to 500 s associated to typical gravity ( g )-modes. From follow-up ground-based spectroscopy, we find that both stars have a similar effective temperature ( T eff  = 120 000 ± 10 000 K) and surface gravity (log g  = 7.5 ± 0.5), but a different He/C composition of their atmosphere. On the basis of PG 1159 evolutionary tracks, we derived a spectroscopic mass of M ⋆ = 0.58 −0.08 +0.16   M ⊙ for both stars. Our asteroseismological analysis of TIC 333432673 allowed us to find a constant period spacing compatible with a stellar mass M ⋆  ∼ 0.60 − 0.61  M ⊙ , and an asteroseismological model for this star with a stellar mass M ⋆ = 0.589 ± 0.020 M ⊙ , as well as a seismological distance of d = 459 −156 +188 pc. For this star, we find an excellent agreement between the different methods to infer the stellar mass, and also between the seismological distance and that measured with Gaia ( d Gaia = 389 −5.2 +5.6 pc). For TIC 095332541, we have found a possible period spacing that suggests a stellar mass of M ⋆  ∼ 0.55 − 0.57  M ⊙ . Unfortunately, we have not been able to find an asteroseismological model for this star. Conclusions. Using the high-quality data collected by the TESS space mission and follow-up spectroscopy, we have been able to discover and characterize two new GW Vir stars. The TESS mission is having, and will continue to have, an unprecedented impact on the area of white-dwarf asteroseismology.