This is a workaround and I hope there is (or will eventually be) an easier way to access point cloud data in the API.

Instead of instancing points, create a new object, eg. a cube, go into edit mode, select everything and right click > Merge Vertices > At Center. That way you have an object with a single vertex at world origin.
In your GN tree add a Point Instance node and choose your single vertex object.

In theory we should be able to access the vertices' geometry but for now the geometry is not "real". We need to trick the modifier into creating real geometry. There are multiple nodes for which it will work. I plugged a default and blank Attribute Math node before the modifier output.

Then, we need to access the evaluated mesh, after the GN modifier has been applied. For that we can use the context dependency graph.
import bpy
depsgraph = bpy.context.evaluated_depsgraph_get()
obj = bpy.context.active_object.evaluated_get(depsgraph)
print([v.co for v in obj.data.vertices])
Result :
