  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 give 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 observed by
both Gaia Data Release 3 as well as public spectroscopic surveys: GALAH DR3,
LAMOST DR7 LRS, LAMOST DR7 MRS, APOGEE DR17, RAVE DR6, SDSS DR12 (optical
spectra from BOSS and SEGUE), Gaia-ESO DR5 survey, and Gaia RVS part of Gaia
DR3 release. We use StarHorse for the first time to derive stellar age for
main-sequence turnoff and subgiant branch stars (MSTO-SGB), around 2.5 million
stars with age uncertainties typically around 30%, 15% for only SGB stars,
depending on the resolution of the survey. With the derived ages in hand, we
investigate the chemical-age relations. In particular, the $\alpha$ and
neutron-capture element ratios versus age in the solar neighbourhood show
trends similar to previous works, validating our ages. We use 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 with
the dimensionality reduction technique t-SNE and the clustering algorithm
HDBSCAN. We identify three distinct groups in all three samples. Their
kinematic properties confirm them to be the genuine chemical thick disk, the
thin disk and a considerable number of young alpha-rich stars. 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$\approx$2)
star-forming disks with high dispersion velocities.
