Private persons have been paying VAT on imports already in the EU since forever, the 150€ de minimis in the EU is specifically for the tariffs, but not for the VAT. That means that all private imports from e.g. China already has to be processed by customs, so it's less of a jump for the EU to remove de minimis, since it would only cover small shipments bought by importing companies, who do not pay VAT. And with the limit being a much lower 150€, the number of parcels overall that would have to be processed additionally is substantially less than in the US.
As a reminder because Trump doesn't seem to know the difference, VAT is paid when you buy any product regardless of whether you imported it or not. Tariffs are paid only for imported products.