A study of the Higgs boson decaying into bottom quarks (H → $ b\overline{b} $) and charm quarks (H → $ c\overline{c} $) is performed, in the associated production channel of the Higgs boson with a W or Z boson, using 140 fb$^{−1}$ of proton-proton collision data at $ \sqrt{s} $ = 13 TeV collected by the ATLAS detector. The individual production of WH and ZH with H → $ b\overline{b} $ is established with observed (expected) significances of 5.3 (5.5) and 4.9 (5.6) standard deviations, respectively. Differential cross-section measurements of the gauge boson transverse momentum within the simplified template cross-section framework are performed in a total of 13 kinematical fiducial regions.The search for the H → $ c\overline{c} $ decay yields an observed (expected) upper limit at 95% confidence level of 11.5 (10.6) times the Standard Model prediction. The results are also used to set constraints on the charm coupling modifier, resulting in |κ$_{c}$| < 4.2 at 95% confidence level. Combining the H → $ b\overline{b} $ and H → $ c\overline{c} $ measurements constrains the absolute value of the ratio of Higgs-charm and Higgs-bottom coupling modifiers (|κ$_{c}$/κ$_{b}$|) to be less than 3.6 at 95% confidence level.[graphic not available: see fulltext]