I’ve written extensively on the topic in other places. Not long ago, it wasn’t a problem to sell through Amazon etc, even if the sale took place on Shabbos. There is no issue of Melacha, since you are not doing anything, and at least in Chutz l’Aretz it can be assumed the buyer is not Jewish. Nevertheless, there remains the problem of deriving benefit from a transaction conducted on Shabbos. However, since then all of the merchants utilized typical credit card processors, who only process charges 5 days a week, no transfer of funds was ever conducted on Shabbos (though a weekday Yom Tov would be problematic).
Today, most merchants use PayPay or another electronic processor, and even the traditional ones have to compete. This means that an approved merchant receives the funds in his bank account within hours, if not minutes, of the sale. This is not permitted.
While it might theoretically be possible to avoid becoming an “approved” merchant and retain a delay of a couple of days between the transaction and the transfer of funds, it is not practical. Furthermore, Amazon will not allow a merchant to close his store one day every week. If one has minimal volume, he could instruct his program to record all Shabbos orders for manual processing on Sunday, but this is not feasible with a large seller. If one could only use a processor who does not transfer funds on Shabbos there would be a Heter.
The Star-K website used to have a Teshuva from Rav Heinemann permitting ecommerce sites on Shabbos based on 5 day/week processors; when I pointed out to him that this is an achronism, they immediately removed the article from their site.