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As far as I understand the decision is about US being able to order companies inside the US, to give them any data, even when that data origins from overseas.

So regarding your question, I guess the answer would be: A European website makes use only of services, which are not in danger of the US (or other countries from outside Europe) ordering the company to grant them access to the data. I guess this means, that you cannot use any services, which are offered by companies, which store data in the US and possibly even if they store it elsewhere, but fall under US law.

It's about the user, not the website.

I'd guess a "European website" stands for a website that safeguards EU users by being compliant with GDPR.

Basically the GDPR considers anything that's accessible or marketed to EU residents (not citizens) under its jurisdiction. In practice this is (probably) pretty much every side that isn't a local business or specifically blocking visitors from the EU.