The full Gaia colour-magnitude diagram with white dwarfs reveals a declining Milky Way star formation history

White dwarfs (WDs) provide a fossil record of the Milky Way star formation history (SFH) through the combined effects of stellar evolution and cooling. They have, however, generally been modelled in isolation from the non-degenerate population, so that no single self-consistent set of Galactic assumptions has been required to reproduce both. We present CALOMERA, a semi-analytic chemo-dynamical population synthesis framework in which the vertical density profiles of mono-age subpopulations are computed self-consistently with the Galactic potential and coupled to modern WD cooling sequences, metallicity-dependent progenitor lifetimes and synthetic photometry. We calibrate 18 parameters describing the initial mass function, SFH, initial-final mass relation and WD population against a Gaia DR3 sample of 7.98×10⁶ stars within 1 kpc, including 1.1×10⁵ WDs. The calibrated model reproduces the star counts in each colour-magnitude diagram region to within 3% and the total number count to within 0.5%, compared with the 81% excess in the predicted WD count obtained with the previous main-sequence-only calibration. The recovered SFH peaks early, declines exponentially thereafter, and includes two recent bursts, located at τ≈2.4 and $0.5$ Gyr. Three cooling libraries (Montréal, BaSTI and LPCODE) yield comparably good fits, with differences confined to MG15 mag. The predicted luminosity function is in reasonable agreement with the 100 pc Gaia WD sample. We further predict the Galactic WD distribution and differential number counts for surveys of varying depth. Extending the framework to the substellar regime using ATMO models, we predict the Galactic L, T, and Y dwarf populations and their contribution to the deep JWST fields.