Unveiling the Milky Way with a Gaia DR3 census of OB-type stars within 2 kpc. I. Tracing local Galactic structure, massive star-forming regions and core-collapse supernova progenitors
O- and B-type stars are young and hot, thereby serving as vital tracers of the star formation and spiral arm structure of the Milky Way. At the dusk of the \textit{Gaia} DR3 era, a high-confidence and accurate catalogue appears timely. Here we have characterized a population of 105,971 OB-type stars (T$_{\rm eff} >$ 10,000 K; hereafter OB stars) within 2 kpc from the Sun, using an astro-photometric Bayesian inference tool. Our resulting map unveils a complex view of the young stellar populations across the thin disk, with prominent large-scale features such as the Cepheus Spur, the Giant Oval Cavity, and a segment of the Sagittarius-Carina spiral arm all visible. Their inhomogeneous spatial distribution implies that massive star formation has taken place clustered across a few highly concentrated regions. We find a correlation between the overdensities of OB stars and young open clusters ($<$20 Myr), although OB stars can be better detected in high-extinction regions. We identify over 4200 OB stars as core-collapse supernova (ccSN) or direct-collapse black hole (BH) progenitor candidates, and therefore targets of interest for spectroscopic follow-up. Furthermore, we find no OB-type star ccSN progenitor to explode within the next 1 Myr within 100 pc, at which such an event could be harmful to Earth's biosphere. Finally, we identify more BH progenitors to collapse within the next 1 Myr than ccSN to explode, despite the former's much scarcer number - which could be indicative of a recent massive star formation burst in the local Milky Way.