A search is reported for pairs of light Higgs bosons (H$_1$) produced in supersymmetric cascade decays in final states with small missing transverse momentum. A data set of LHC pp collisions collected with the CMS detector at $\sqrt{s}$ = 13 TeV and corresponding to an integrated luminosity of 138 fb$^{-1}$ is used. The search targets events where both H$_1$ bosons decay into $\mathrm{b\bar{b}}$ pairs that are reconstructed as large-radius jets using substructure techniques. No evidence is found for an excess of events beyond the background expectations of the standard model (SM). Results from the search are interpreted in the next-to-minimal supersymmetric extension of the SM, where a "singlino" of small mass leads to squark and gluino cascade decays that can predominantly end in a highly Lorentz-boosted singlet-like H$_1$ and a singlino-like neutralino of small transverse momentum. Upper limits are set on the product of the squark or gluino pair production cross section and the square of the $\mathrm{b\bar{b}}$ branching fraction of the H$_1$ in a benchmark model containing almost mass-degenerate gluinos and light-flavour squarks. Under the assumption of an SM-like H$_1$$\to$$\mathrm{b\bar{b}}$ branching fraction, H$_1$ bosons with masses in the range 40-120 GeV arising from the decays of squarks or gluinos with a mass of 1200 to 2500 GeV are excluded at 95% confidence level.
Reference acceptance times efficiency values for the kinematic selection and $H_T>3500\;\mathrm{GeV}$ requirements ($A_{\mathrm{kin}}$) for the benchmark signal model with different values of $m_{\mathrm{SUSY}}$. These values are independent of $m_{\mathrm{H_1}}$ within 2% in the range $30 \le m_{\mathrm{H_1}} \le 125\;\mathrm{GeV}$.
Upper limits at 95% CL on $\sigma\times\mathcal{B}^2(\mathrm{H}_1\rightarrow b\bar{b}) \times A_{\mathrm{kin}}$ as a function of $m_{\mathrm{H_1}}$. The results are independent of $m_{\mathrm{SUSY}}$ within 10% in the range $1600<m_{\mathrm{SUSY}}<2800\;\mathrm{GeV}$.
Upper limits at 95% CL on $\sigma\times\mathcal{B}^2(\mathrm{H}_1\rightarrow b\bar{b})$ as a function of $m_{\mathrm{H_1}}$ for $m_{\mathrm{SUSY}}=1200\;\mathrm{GeV}$.
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