In training a mushroom vs. non-mushroom image classifier, which images should comprise the negative class?
Only you can answer this question. The answer requires some careful thinking on your part, and it depends on what types of objects that you believe your classifier will encounter once deployed in the "real world". If you are only going to present "vegetation" to your classifier, then you probably only need to curate a mushroom (positive class) and plant (negative class) dataset. On the other hand, if there are no limits to what your classifier will encounter, then your training images for the non-mushroom class must include the visible universe (minus the mushrooms, of course). Ideally, your positive and negative class images should be collected in the same manner, at least how they would be collected when implemented.
On a broader level, the problem that you pose is a form of binary classification. The image classification problems dog vs. cat and dog vs. not dog are both binary classification problems. On the one hand, cats are similar to dogs, so one may argue that this problem is more difficult. On the other hands, the problem of learning a representation of not dog is challenging, as it can represent many different things, and is practically difficult, as it requires capturing the universe of all things not dog. Although, in practice, only images that are likely to be used at inference are worth curating for the not dog category.