* https://rewis.io/urteile/urteil/lhm-20-01-2022-3-o-1749320/
* https://www.cnil.fr/en/use-google-analytics-and-data-transfe...
* https://www.gpdp.it/web/guest/home/docweb/-/docweb-display/d...
So far they've just been enforced against companies that use Google Analytics, but the reasoning behind it has been that having users connect to a US server enables that server to know EU users' IP addresses (which are legally PII), which would be subject to US government subpoenas to collect such, and the US government has not agreed to handle data in compliance with the GDPR, therefore it's illegal to have users connect to any US servers. It has nothing to do with "hoover[ing] and hoard[ing]" data.
The only way for an American website to comply would be to form a separate company not subject to US control at all. However, at that point it's not really an American website, since no data or control can go to the US.
Theoretically you could use some international service to handle all primary routing and get users to waive their rights under the GDPR before connecting to your website proper, but I'm not aware of such a service at this time.