How to get the shop up and running
Your page looks very nice and polished, congratulations.
I took the liberty to look at the page source of your site. Well, in a way it does answer my question "where does the data go?", because every item you present on the grid has a basket icon that is an HTML FORM that communicates to Paypal, so Paypal holds the cart, do I understand this correctly?
Now thats an entirely different ballgame. I never had a closer look at one of Paypals contracts for sellers, but speaking in GDPR terms that means joint controllership of Paypal and the seller to the entire (personal) data even before a customer actually clicks on checkout...