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The third data release of Gaia has provided low resolution spectra for ~100,000 white dwarfs (WDs) that, together with the excellent photometry and astrometry, represent an unrivalled benchmark for the study of this population. In this work, we first built a highly-complete volume-limited sample consisting in 12,718 WDs within 100 pc from the Sun. The use of VOSA tool allowed us to perform an automated fitting of their spectral energy distributions to different atmospheric models. In particular, the use of spectrally derived J-PAS photometry from Gaia spectra led to the classification of DA and non-DA WDs with an accuracy >90%, tested in already spectroscopically labelled objects. The excellent performance achieved was extended to practically the whole population of WDs with effective temperatures above 5500 K. Our results show that, while the A branch of the Gaia WD Hertzsprung-Russell diagram is practically populated by DA WDs, the B branch is largely formed by non-DAs (65%). The remaining 35% of DAs within the B branch implies a second peak at ~0.8 Mo in the DA-mass distribution. Additionally, the Q branch and its extension to lower temperatures can be observed for both DA and non-DA objects due to core crystallisation. Finally, we derived a detailed spectral evolution function, which confirms a slow increase of the fraction of non-DAs as the effective temperature decreases down to 10,500 K, where it reaches a maximum of 36% and then decreases for lower temperatures down to ~31%.