Use free/libre software, running on your own server, and don’t use any 3rd party services besides the payment processor(s).

The site you’re referring to appears to be built using WordPress with https://en.wikipedia.org/wiki/WooCommerce btw.

just do a basic check on the based.win shop, whole page is funneled via cdn (bunny cdn), they have analytics, so not true they are not tracking, there is also woocommerce wordpress plugin, makes me wonder, the page is running on wordpress? the path is /wp-plugins/woocommerce, meaning there is wordpress core, so where is the cookie banner? maybe its forked wp core, idk. but the whole punch with no tracking is questionable.

hosting, you can host it at home server, its more difficult but you can still do it, if someone will ddos you you will have a fun time.

you can still host on privacy friendly VPS, or just other hosting service, just read contract. Hosters usually dont scale customers data, for sure they will have ip addresses, but that will be also visible to your IPS when hosting from home server.

as a shop platform, clean php core and for front end some js. Like were 10y ago, lol. everything served as 1st party, no loading out from page, no google fonts, no third party scripts and bullshits, plugins.

own cache, own ssl, own seo, no cloudflare, no cdn, and it could go on for a while.

it a shop, business needs to have stats, so if you sit on bunch of money no problem, but if you like to have ypur biz up and survive, then you need to know where the customers cliking, where they come from and what is hot for them.

good luck,

I guess this depends how you define privacy. One solution may be Particl, but I haven’t tried it so far.

Without giving out your info?