Detection of black holes (BHs) with detached luminous companions (LCs) can be instrumental in connecting the BH properties with their progenitors' since the latter can be inferred from the observable properties of the LC. Past studies showed the promise of Gaia astrometry in detecting BH-LC binaries. We build upon these studies by: 1) initialising the zero-age binary properties based on realistic, metallicity-dependent star-formation history in the Milky Way (MW), 2) evolving these binaries to current epoch to generate realistic MW populations of BH-LC binaries, 3) distributing these binaries in the MW preserving the complex age-metallicity-Galactic position correlations, 4) accounting for extinction and reddening using three-dimensional dust maps, 5) examining the extended Gaia mission's ability to resolve BH-LC binaries. We restrict ourselves to detached BH-LC binaries with orbital period <10 yr such that Gaia can observe at least one full orbit. We find: 1) the extended Gaia mission can astrometrically resolve 30-300 detached BH-LC binaries depending on our assumptions of supernova physics and astrometric detection threshold; 2) Gaia's astrometry alone can indicate BH candidates for 10-100 BH-LC binaries by constraining the dark primary mass >3 Msun; 3) distributions of observables including orbital periods, eccentricities, and component masses are sensitive to the adopted binary evolution model, hence can directly inform binary evolution models. Finally, we comment on the potential to further characterise these BH binaries through radial velocity measurements and observation of X-ray counterparts.