A search for nonresonant Higgs boson pair production in the
$b\bar{b}\gamma\gamma$ final state is performed using 140 fb$^{-1}$ of
proton-proton collisions at a centre-of-mass energy of 13 TeV recorded
by the ATLAS detector at the CERN Large Hadron Collider.
This analysis supersedes and expands upon the
previous nonresonant ATLAS results in this final state based on the
same dataset.
The analysis strategy is optimised to probe anomalous values not only of the
Higgs ($H$) boson self-coupling modifier $\kappa_\lambda$ but also
of the quartic $HHVV$ ($V=W,Z$) coupling modifier $\kappa_{2V}$.
No significant excess above the expected background from
Standard Model processes is observed. An observed upper limit
$\mu_{HH}<4.0$ is set at 95\% confidence level on the Higgs boson
pair production cross-section normalised to its Standard Model prediction.
The 95\% confidence intervals for the coupling modifiers
are $-1.4< \kappa_\lambda <6.9$ and $-0.5< \kappa_{2V} <2.7$,
assuming all other Higgs boson couplings
except the one under study are fixed to the Standard Model predictions.
The results are then interpreted in the Standard Model effective field
theory and Higgs effective field theory frameworks in terms of
constraints on the couplings of anomalous Higgs boson
(self-)interactions.