I'm on Fastmail. I looked back at some of my old Gmail emails and they do list items. The Fastmail emails do not. This strikes me as really weird, if anything I would expect it to be the opposite.

Regardless, it's pretty clear that Amazon doesn't universally hide order information, so my assertion that they're doing it to avoid Gmail tracking seems to be pretty objectively wrong. If they were, they would do a better job.

Note that Gmail is still tracking your purchases, that's pretty widely established, and until recently, they were using your purchase history for ads. But I'm definitely wrong about Amazon's response, and I can't track down whatever source gave me that idea.