I've started to be a big fan of store-bought spicy ajvar, which is generally a delicious and low-effort spread for toast et al.
However, all the jars claim something like "after opening, refrigerate and consume within 3-4 days", despite being essentially lightly pickled, cooked peppers and seem perfectly fine to consume through about the 4-weeks mark (about the 4-5 week mark, I've seen visible molding, which more pickled foods like kosher pickles, kimchi, etc. don't display .. though this mold is probably still safe to eat, it probably tastes bad and should be discarded)
Why do retailers suggest such a brief edible range? Is it really fine to eat?