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. We have characterized 105,971 OB-type stars (T$_{\rm eff} >$ 10,000 K) within 2 kpc from the Sun, using an astro-photometric Bayesian inference tool. Our 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 the Sagittarius-Carina 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-type stars and young open clusters, and attribute departure from it to extinction effects. We identify 4200 stars as model-dependent core-collapse supernova (ccSN) or direct-collapse black hole (BH) progenitor candidates, including 6 ccSN progenitor candidates within 125 pc -- the maximum radius within which a ccSN explosion could be harmful to Earth's biosphere -- but our analysis suggests none of them exploding within the next 5 Myrs. Finally, we anticipate more evolved OB-type stars to collapse to form BHs within the next 1 Myr than ccSN progenitors will explode, despite the former's much scarcer number. A possible interpretation is a recent star formation burst in the local Milky Way, consistent with overdensities of ccSN progenitor candidates in Cyg OB2 and the Sagittarius-Carina arm.