The result of a search for the pair production of the supersymmetric partner of the bottom-quark ($\tilde{b}$) using 139 fb$^{-1}$ of data collected at $\sqrt{s} = 13$ TeV by the ATLAS detector in Run 2 is reported. In the supersymmetric scenarios considered, each of the bottom-squarks decay to a $b$-quark and the second lightest neutralino, $\tilde{b} \rightarrow b + \tilde{\chi}_{2}^{0}$. Each $\tilde{\chi}_{2}^{0}$ is assumed to subsequently decay with 100% branching ratio to the Standard-Model-like Higgs boson ($h$) and the lightest neutralino: $\tilde{\chi}_{2}^{0} \rightarrow h + \tilde{\chi}_{1}^{0}$. The $\tilde{\chi}_{1}^{0}$ is assumed to be the lightest supersymmetric particle (LSP) and is stable. Two signal mass configurations are targeted: the first has a constant LSP mass of 60 GeV; and the second has a constant mass difference between the $\tilde{\chi}_{2}^{0}$ and $\tilde{\chi}_{1}^{0}$ of 130 GeV. The final states considered contain no charged leptons, three or more $b$-jets, and large missing transverse momentum. No significant excess of events over the Standard Model background expectation is observed in any of the signal regions considered. Limits at the 95% confidence level are placed in the supersymmetric models considered, and bottom-squarks with mass up to 1.45 TeV are excluded.

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