In my experience (europe) delivery companies get access to my unique email address that I also only use to buy things on amazon. They use this email address to send me information about deliveries directly to my inbox.
All the info is being skimmed and sold at some point. It often mentions the parcel company it arrives through which confirms this to me.
Third-party sellers are typically given an address like <gibberish-hash>@marketplace.amazon.com to which they can reply, and correspondence is then forwarded by Amazon to the actual customer's email.
* there was no obvious way to do it. Closest thing was by reporting issue on product.
* there was no way to show the customer service agent a picture of the mail. Chat did not support sending pictures & they were unable to open imgur link.
* agent recommended me to leave a report it by leaving review to the seller page. I did that and next day review was deleted.
(I must admit I created them approx 100 USD/EUR turnover last year and 20 USD/EUR this year. Sometimes all alternatives are so much worse.)
But yes, some couriers do let you tie an email address to a physical address to get notifications.