  The aim of this paper is twofold. We first present a construction of
overconvergent automorphic sheaves for Siegel modular forms by generalising the
perfectoid method, originally introduced by Chojecki-Hansen-Johansson for
automorphic forms on compact Shimura curves over $\mathbf{Q}$. These sheaves
are then verified to be isomorphic to the ones introduced by
Andreatta-Iovita-Pilloni. Secondly, we establish an overconvergent
Eichler-Shimura morphism for Siegel modular forms, generalising the result of
Andreatta-Iovita-Stevens for elliptic modular forms.
