As correctly stated by the guys in blender.chat, the #python channel, storing attributes in Curve Shapes is not useful because it cannot be retrieved. In order to be able to use an attribute that you have previously stored onto the geometry, you need to store it in a Mesh Shape/Transform object type.
So the solution for me, was to create a new Node Group with all the GN Network and reuse it in a "dummy" geometry cube where, with its own GN network, i would inject the stored value into a new "Store Named Attribute" this time on the cube Mesh Shape.... and voilà.
Having understood this, the next step is to use a function that reads the "AngleBetweenVectors" parameter and substracts it to the "offset" parameter of a Follow Path Constraint. This, done by means of a Driver.
This last step is making Blender 4.1.1 crash when i hit "update dependencies". Not sure yet what the problem could be. Most probably with the "evaluation of the graph", being it maybe "cyclic". Not sure yet.