Amazon parser, how to change shipping addresses?

Question

Delivery

Hello!
When parsing an amazon product page, the same product may change price or availability depending on what is selected in the "Deliver To" field (top left, near the Amazon logo).
When changing address, Amazon sends an asynchronous request to https://www.amazon.co.uk/gp/delivery/ajax/address-... with certain parameters. I've been fighting for a day, and the parameters are the same, and the response is 200 from the page and the cookies are the same. But the next time the product page is parsed, the country remains the same.
I use python requests (session).

I would like to know if this works for someone without selenium, etc.? just on get/post requests with cookies and correct headers?