I have never ever seen a Royal Mail van making deliveries on a Sunday. Amazon, yes, their van is round every week. But Royal Mail usually deliver Monday to Friday, and perhaps Saturday if you're lucky. Years ago, Royal Mail had two delivery rounds but it's a long time since they cut back to just one.
I don't know how things work in the US, but here in the UK we have Royal Mail which delivers letters and small parcels. They drive to your street, park up then walk up and down the street with a bag over their shoulder posting things through the letterbox in front doors. Then there are a number of other couriers who only deliver parcels. Amazon, DPD, Yodel, Evri etc etc. They drive to each house to make a delivery. The main difference is that almost every house gets something delivered by Royal Mail every day, be it a letter, a bill or a birthday card (or junk mail) but the couriers deliver only to one or two houses per day in a street.
All we had delivered was the bill for the boiler service a couple of days ago.