  We prove the existence of global-in-time regular solutions to a system of
stochastic quadratic reaction-diffusion equations. Global-in-time existence is
based on a $L^\infty$-estimate obtained by an approach {\`a} la De Giorgi, as
in [GoudonVasseur10]. The adaptation of this technique to the stochastic case
requires in its final step an $L^2\ln(L^2)$-bound, furnished by an estimate by
duality on the entropy inequality, as in [DesvillettesFellnerPierreVovelle07].
In our stochastic context, and similarly to [DebusscheRoselloVovelle2021], we
need to solve a backward SPDE to exploit the duality technique
