A search for the resonant production of a heavy scalar $X$ decaying into a Higgs boson and a new lighter scalar $S$, through the process $X \to S(\to bb) H(\to \gamma\gamma)$, where the two photons are consistent with the Higgs boson decay, is performed. The search is conducted using an integrated luminosity of 140 fb$^{-1}$ of proton-proton collision data at a centre-of-mass energy of 13 TeV recorded with the ATLAS detector at the Large Hadron Collider. The search is performed over the mass range 170 $\leq$$m_{X}$$\leq$ 1000 GeV and 15 $\leq$$m_{S}$$\leq$ 500 GeV. Parameterised neural networks are used to enhance the signal purity and to achieve continuous sensitivity in a domain of the ($m_{X}$, $m_{S}$) plane. No significant excess above the expected background is found and 95% CL upper limits are set on the cross section times branching ratio, ranging from 39 fb to 0.09 fb. The largest deviation from the background-only expectation occurs for ($m_{X}$, $m_{S}$) = (575, 200) GeV with a local (global) significance of 3.5 (2.0) standard deviations.
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