How does my VAT ID affect the price?

Your nouz plan is part of your Shopify bill, so tax on it is Shopify's to apply. Shopify adds whatever tax it must charge in your region.

Your VAT ID is kept in your Shopify account, not in nouz. A VAT ID is the tax number of a business in the EU. Whether it changes the tax on your bill, for example through reverse charge, follows Shopify's rules for your country. You manage it in your Shopify admin.

The plan prices nouz shows are net, which means before tax. So the total on your Shopify bill can be higher than the price on the pricing page.