In order to answer your question, we will have to investigate some of the concepts that you correctly cite and see how they apply to your case.
One does not have to make a separate beracha on every food he eats, even if it is not part of a meal that began with bread. Rather a beracha can pertain to any other food that he will eat at that sitting which shares the same beracha.[1] The idea is that when one makes a beracha, he has some level of intention that it should cover other foods that he might eat later.[2]
It is also true that Shehakol works for foods that should have gotten a different beracha. This is part of a rule that more general berachot work b’di’eved for foods for which a more specific and, therefore, preferable beracha should have been said.[3]
When we put these two facts together, we have the following problem. If one makes a Shehakol on milk and then is about to eat cookies, why should he make a beracha on them? After all, doesn’t the Shehakol which he said already exempt (b’di’eved) even cookies from a beracha? Rashi[4] answers that the idea of being yotzei with the more general beracha applies only when one makes it mistakenly on a certain food, but it does not extend to exempt other foods with the more specific beracha. Rabbeinu Yona[5] says that it actually all depends on intention. If one correctly says HaAdama on a vegetable, there is no reason to assume he intended to include a fruit that he will eat at the same sitting for which HaEtz is the correct beracha. The Shulchan Aruch,[6] adopting Rabbeinu Yona’s approach, says that if, for some reason, one intended to use the beracha of HaAdama not only for the vegetable but also for a fruit that was there, then he would not make another beracha on the fruit.
Along similar lines, one who makes a Shehakol on something that actually requires a Mezonot usually intends to include not only that food, but all foods that require a Shehakol. Therefore, he exempts them all.[7] As we have seen, it is his inclusive intention that is crucial and overcomes the fact that the new “Shehakol foods” he desires to eat have a different beracha from the food on which he mistakenly made Shehakol. On the other hand, foods that require Mezonot are not exempted. The reason is that he did not have them in mind when making Shehakol because the Shehakol he was reciting was not the optimal beracha for them.
The more interesting question regards foods that share the beracha that he made, yet he presumably did not have them in mind. This can occur if one intended to correctly say Mezonot, and Shehakol slipped out. In this case, the Har Tzvi[8] says that since he intended the beracha for Mezonot foods, Shehakol foods are not included, and they would require a new beracha. He implies, and Piskei Teshuvot[9] states, that Mezonot foods are covered with that Shehakol because he intended to exempt Mezonot foods and made a beracha that works for them, b’di’eved.
The situation may be different for foods that were not present when the mistaken beracha was made, but that discussion is beyond our present scope.