And to the point of the discussion, there are no "limits" to what jurisdiction governments have. Governments--the United States especially but many others--does it all the time, especially as concerns financial matters. Many countries have declared that they have jurisdiction over crimes against humanity committed any time, anywhere, by anyone. China has penalized American companies for activities involving Americans in America.
However the EU probably has self-imposed limits (or imposed by the member states) and as a practical matter only large or powerful states can get away with it.