Context. Gaia Bp/Rp spectrophotometry for over two hundred million stars has been publicly released as part of Gaia Data Release 3 (DR3). These data have great potential for mapping metallicity across the Milky Way. Several recent studies have analyzed this data set to derive atmospheric parameters and identify new metal-poor stars. In addition, systematics in the fluxes of the Bp/Rp spectra have also been identified and characterized. Aims. We aim to construct an alternative catalog of atmospheric parameters from Gaia Bp/Rp spectra by fitting them with synthetic spectra based on model atmospheres, and provide corrections to the Bp/Rp fluxes according to stellar colors, magnitudes, and interstellar extinction. Methods. We use GaiaXPy to obtain calibrated spectra and apply FERЯ to match the corrected Bp/Rp spectra with models and infer atmospheric parameters. We train a neural network (NN) using stars in the Apache Point Observatory Galactic Evolution Experiment (APOGEE) to predict flux corrections as a function of wavelength for each target. Results. Based on the comparison with APOGEE parameters, we conclude that our estimated parameters have systematic errors and uncertainties in Teff, log g, and [M/H] about ‑38 ± 167 K, 0.05 ± 0.40 dex, and ‑0.12 ± 0.19 dex, respectively, for stars in the range 4000 ≤ Teff ≤ 7000 K. The corrected Bp/Rp spectra show improved agreement with both models and Hubble Space Telescope (HST) CALSPEC data. Our correction increases the precision of the relative spectrophotometry of the Bp/Rp data from 3.2–3.7% to 1.2–2.4%. We also compare our results with other similar catalogs from the literature and validate them using star clusters. Finally, we have built a catalog of atmospheric parameters for stars within 4000 ≤ Teff ≤ 7000 K, comprising 68 394 431 sources, along with a subset of 124 188 stars with [M/H] ≤ ‑2.5. Our catalogs and flux correction code are publicly available. Conclusions. Our results confirm that the Gaia Bp/Rp flux calibrated spectra show systematic patterns as a function of wavelength that are tightly related to colors, magnitudes, and extinction. Our optimization algorithm can give us accurate atmospheric parameters of stars with a clear and direct link to models of stellar atmospheres, and can be used to efficiently search for extremely metal-poor (EMP) stars.