We report on the results obtained with the global CUPID-0 background model, which combines the data collected in the two measurement campaigns for a total exposure of 8.82 kg×yr of ^{82}Se. We identify with improved precision the background sources within the 3 MeV energy region, where neutrinoless double β decay of ^{82}Se and ^{100}Mo is expected, making more solid the foundations for the background budget of the next-generation CUPID experiment. Relying on the excellent data reconstruction, we measure the two-neutrino double β-decay half-life of ^{82}Se with unprecedented accuracy: T_{1/2}^{2ν}=[8.69±0.05(stat)_{-0.06}^{+0.09}(syst)]×10^{19} yr.