Your link says exactly the same as mine.@mysiak, from 1st July 2021 online EU sellers are required to apply VAT rates at the customer's country rates.
https://europa.eu/youreurope/business/taxation/vat/cross-border-vat/index_en.htm
"If you are an online seller, including on online marketplaces and platforms, you canāÆregisterāÆin one EU country for the declaration and payment of VAT on all distance sales of goodsāÆand cross-border supplies of services to customers in the EU.
Example 3: When goods supplied are subsequently transported from Bratislava to a customer in Prague by the customer or by a transporter appointed by him, the supply will be subject to Slovakian VAT."
So in this particular case, Vapman would display price with VAT, collect it in Italy and there will be no other tax or VAT collected at checkout for EU customers (as is the case with practically all other EU shops). Shipping destination doesn't matter as long as it's in EU.