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This Letter reports measurements of muon-neutrino disappearance and electron-neutrino appearance and the corresponding antineutrino processes between the two NOvA detectors in the NuMI neutrino beam. These measurements use a dataset with double the neutrino mode beam exposure that was previously analyzed, along with improved simulation and analysis techniques. A joint fit to these samples in the three-flavor paradigm results in the most precise single-experiment constraint on the atmospheric neutrino mass splitting, $\mathrm{\Delta }{m}_{32}^2=2.431_{-0.034}^{+0.036}(-2.479_{-0.036}^{+0.036})\times {10}^{-3}{\mathrm{eV}}^2$if the mass ordering is normal (inverted). In both orderings, a region close to maximal mixing with ${\sin }^2{\theta }_{23}=0.55_{-0.06}^{+0.02}$is preferred. The NOvA data show a mild preference for the normal mass ordering with a Bayes factor of 2.4 (corresponding to 70% of the posterior probability), indicating that the normal ordering is 2.4 times more probable than the inverted ordering. When incorporating a 2D $\mathrm{\Delta }{m}_{32}^2-{\sin }^{2}2{\theta }_{13}$constraint based on Daya Bay data, this preference strengthens to a Bayes factor of 6.6 (87%).