Currently, the w3c context propagation is not tested. As per @mauriciovasquezbernal's comment we can use the same tests as the opentelemetry-python repo:

There is this https://github.com/w3c/trace-context/tree/master/test.
It's used in opentelemetry-python: open-telemetry/opentelemetry-python#228.
The idea is to follow a similar approach here and use that for testing the w3c.