The Gaia mission has provided an invaluable wealth of astrometric data for more than a billion stars in our Galaxy. The synergy between Gaia astrometry, photometry, and spectroscopic surveys gives us comprehensive information about the Milky Way. Using the Bayesian isochrone-fitting code StarHorse, we derive distances and extinctions for more than 10 million unique stars listed in both Gaia Data Release 3 and public spectroscopic surveys: 557 559 in GALAH+ DR3, 4 531 028 in LAMOST DR7 LRS, 347 535 in LAMOST DR7 MRS, 562 424 in APOGEE DR17, 471 490 in RAVE DR6, 249 991 in SDSS DR12 (optical spectra from BOSS and SEGUE), 67 562 in the Gaia-ESO DR5 survey, and 4 211 087 in the Gaia RVS part of the Gaia DR3 release. StarHorse can increase the precision of distance and extinction measurements where Gaia parallaxes alone would be uncertain. We used StarHorse for the first time to derive stellar ages for main-sequence turnoff and subgiant branch stars, around 2.5 million stars, with age uncertainties typically around 30%; the uncertainties drop to 15% for subgiant-branch-only stars, depending on the resolution of the survey. With the derived ages in hand, we investigated the chemical-age relations. In particular, the α and neutron-capture element ratios versus age in the solar neighbourhood show trends similar to previous works, validating our ages. We used the chemical abundances from local subgiant samples of GALAH DR3, APOGEE DR17, and LAMOST MRS DR7 to map groups with similar chemical compositions and StarHorse ages, using the dimensionality reduction technique t-SNE and the clustering algorithm HDBSCAN. We identify three distinct groups in all three samples, confirmed by their kinematic properties: the genuine chemical thick disk, the thin disk, and a considerable number of young alpha-rich stars (427) that are also a part of the delivered catalogues. We confirm that the genuine thick disk's kinematics and age properties are radically different from those of the thin disk and compatible with high-redshift (z ≈ 2) star-forming disks with high dispersion velocities. We also find a few extra chemical populations in GALAH DR3 thanks to the availability of neutron-capture element information.

Data are only available at the CDS via anonymous ftp to cdsarc.cds.unistra.fr (ftp://130.79.128.5) or via https://cdsarc.cds.unistra.fr/viz-bin/cat/J/A+A/673/A155