Based on what I've read and this article, it doesn't sound like that much will change once it officially "launches" a Swedish site, although maybe Amazon will lower the minimum amount for free shipping or speed up regular shipping time. Re: this article, I can see them being willing to hold off for quite some time.
Also to note: During the Covid-19 peak in Sweden, Amazon provided to-the-door delivery using Postnord, which I figured was somewhat of an experiment for when the Swedish site launched. It's pretty rare here in e-commerce to get door deliveries - most online shopping is sent to local convenience stores and you need to go and pick up.