Learn Finnish: Tämä ruoka ei sisällä yhtään proteiinia, mutta ainakin se antaa energiaa. - This food does not contain any protein, but at least it gives energy.

Even though both mean "at least", they are used differently. Vähintään is strictly for measurable quantities and numbers (like "at least 10 grams"). Ainakin is used for subjective minimums, emphasis, or pointing out a silver lining, which is exactly what is happening here: it lacks protein, but at least it gives energy.

Why do we use yhtään here for "any" instead of mitään?

In negative sentences, yhtään is used to mean "any at all" when talking about amounts, especially with uncountable mass nouns like proteiinia. While ei mitään (nothing / not any) is common, ei yhtään is the most natural way to emphasize a quantity of absolutely zero for a substance.

Why are both proteiinia and energiaa in the partitive case?

For proteiinia, there are two reasons: the sentence is negative (ei sisällä), and the verb sisältää (to contain) naturally requires a partitive object. For energiaa, it is the object of antaa (to give), and because energy is an uncountable mass noun (it gives an unspecified amount of energy, not a single whole "energy"), it must be partitive.

Could ainakin be moved to the end of the sentence?