  This Letter presents results from a combination of searches for Higgs boson
pair production using 126$-$140 fb$^{-1}$ of proton$-$proton collision data at
$\sqrt{s}=13$ TeV recorded with the ATLAS detector. At 95% confidence level
(CL), the upper limit on the production rate is 2.9 times the Standard Model
(SM) prediction, with an expected limit of 2.4 assuming no Higgs boson pair
production. Constraints on the Higgs boson self-coupling modifier
$\kappa_{\lambda}=\lambda_{HHH}/\lambda_{HHH}^\mathrm{SM}$, and the quartic
$HHVV$ coupling modifier $\kappa_{2V}=g_{HHVV}/g_{HHVV}^\mathrm{SM}$, are
derived individually, fixing the other parameter to its SM value. The observed
$95%$ CL intervals are $-1.2 < \kappa_{\lambda} < 7.2$ and $0.6 < \kappa_{2V} <
1.5$, while the expected intervals are $-1.6 < \kappa_{\lambda} < 7.2$ and $0.4
< \kappa_{2V} < 1.6$ in the SM case. Constraints obtained for several
interactions within Higgs effective field theory are the strongest to date,
offering insights into potential deviations from SM predictions.
