Возможно, родным языком подошло бы больше, но «мягкий контейнер» не приживается на рабочих просторах

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аргументирую:

A tote bag is a large handheld bag or purse that is used to carry things, such as books, beach wear, or everyday items. A tote bag is normally made of treated canvas, nylon or heavy pebbled leather[1]. Some totes come with a zipper compartment that divides the bag into sections. The term tote, meaning "to carry" can be traced back to the 17th century but was not used to describe bags until 1900[2].

Several chains of supermarkets offer reusable bags, often made of cotton, as an alternative to paper or plastic shopping bags. These are often labeled tote bags and sometimes also canvas tote bags to highlight their durability.