  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.
