to replicate a component of an Actor, like the static Mesh, you need to select the component and search in the detail Panel for “Replicate Component” and set it to true (a checkbox).
The Actor itself needs to be replicated, too.
important to know:
you need to set the mesh on authority side, not client one.
when you set the mesh at client side, the value will not be replicated up, cause replication of values works from server down to client, not vise versa.