Homotopy cartesian squares in extriangulated categories

Let (C,E,s)\left({\mathcal{C}},{\mathbb{E}},{\mathfrak{s}}) be an extriangulated category. Given a composition of two commutative squares in C{\mathcal{C}}, if two commutative squares are homotopy cartesian, then their composition is also a homotopy cartesian square. This covers the result by Mac Lane [Categories for the Working Mathematician, Second edition, Graduate Texts in Mathematics, Vol. 5, Springer-Verlag, New York, 1998] for abelian categories and by Christensen and Frankland [On good morphisms of exact triangles, J. Pure Appl. Algebra 226 (2022), no. 3, 106846] for triangulated categories.