I too was under the impression that there are extra leniencies on shabbat which are granted because of the concept of עונג שבת. However, I was unable to turn up any source for this. In every respect, the laws of shabbat would apply equally to food and non-food items, and as others have pointed out, your example of tearing the bag would apply equally to a bag not containing food needed for shabbat (say, the pieces of a board game).
Incidentally, I remembered learning that the three conditions under which בורר is permitted are the acronym אכ"ל, ochel - אוכל, ביד (ולא בכלי), לאלתר. That is, it must be for food, done by hand and not with a specialised utensil, and done immediately prior to consumption. But in fact the אוכל in that phrase refers to taking the אוכל - good - from the פסולת - bad, and not the other way around. It would apply equally to non-food בורר (say, taking a fork from mixed cutlery for immediate use), but אוכל is just used as the most common example of sorting.
(In fact, some poskim hold that בורר only applies to food.)