@erincandescent @russss @wink having looked up a few businesses' EUIDs , it seems those unique IDs are just X-Justiz IDs.
At least all EUIDs i saw had the form "DE" followed by the X-Justiz ID of the court, followed by a dot and then the HRB.
e.g.: "DEF1103R.HRB74346B" for D-Trust GmBH