What is milk classified as once you pour it on cereal?

TL:DR It has no such status. People just don't really have the need to categorize it, so it doesn't belong to a special category.

You are somewhat mixing up formal classifications and the process of categorization in everyday language usage. Dictionary definitions apply to everyday language, but they don't have a prescriptive status. Due to the way language and human cognition works, you can never come up with exact criteria that define whether an item belongs to a category or not. So looking up random cooking definitions like "sauce" is pointless in this case, even if an item nominally fits a definition, this does not make it belong to the category if people don't perceive it as belonging to the category.

Formal classifications about food do exist. In them, it is quite likely that you will find prescriptive definitions, intended to be used to determine whether an item falls into the category. These definitions have validity only within the framework itself - for example, a tomato falls in the fruit category when you talk to botanists, but not in the classification of foods used by the Culinary institute of America (it so happens that in this case, common language usage is firmly on the side of one of those, but other cases may be more ambiguous). It is a special feature of formal classifications that they only work well on the items they were intended for - E.g. I have seen several American authors categorize cakes by type of batter, and there is no good way to fit a cake made of quark-oil dough into one of those.

Regarding formal categorizations, I cannot think of a categorization framework that has a category into which "the milk in a bowl of cereal" can fit snugly. I cannot think of either a legal context or a scholarly context where that milk will come into discussion at all. In most cases, the mixture is just not perceived as a separate entity - people buy, prepare and serve bowls of cereal with milk as wholes. Also, there is rarely reason to see the milk in the cereal as a member of a category, as opposed to just "the milk".

The one context which might yield something would be books on food technology, concerned either with grain chemistry or with the industrial preparation of cereal products, like a description of the process for making prepackaged cups of yoghurt and cereal. They could have a need to refer to an abstract category which could include milk, yoghurt, or anything else pourable over cereal, and to discuss its physical properties. I have never read such a highly technical book on this topic, but I suspect it would simply use some quite broad category of everyday language such as "the liquid" and implicitly assume that in the context of the text, it is used for any liquid that is being poured over the cereal. It would be interesting if somebody can come up with an example, but it is quite certain that, if you try to use it in everyday life, it won't be perceived as a specific technical term.