All EU has exactly the same law:
If anyone is purchasing gold with value which is over the limit Level 1 set by each EU country differently, seller has to make a
KYC due dilligence about identity of buyer. The most of EU countries has limits between 1000 and 3000 Eur. If your purchase over Level 2, what is 15,000 Eur for all Eu coutries, seller has to make KYC due dilligence also for source of funds. All documents from Dues dilligence has to be stored for at least 10 years from the 1st january of the next year after the year of purchase.
So there is no way how to
buy gold anonymously in EU.
Seller does not report anything. Or to be absoluteluy honest, seller does not report anything unless he does not consider transaction to be used for money laundering or financing terorism. If seller consider transaction to be too risky based on las against money laundering and financing of terorism, there is legal responsibility to inform Financial unit of Police of country where seller resides.