The English here sounds... incredibly unnatural. I understand that you all are trying to emphasize the Partitive here, but 'milkshake' is a very unfortunate choice of example because it is used as if it comes in countable units most of the time. When it is not, I believe it sounds most natural to pair it with "some of [article / determiner / possessive adjective]" i.e. "some of that milkshake" or "some of your milkshake".
I don't want to submit an error report without first seeing if my intuition in this is correct or not. What do others think?
Several people have expressed a similar sentiment about sentences that include the word "milkshake" as this course often seems to treat it like a mass noun, which may be because its Finnish equivalent is a mass noun. However, "milkshake" is generally countable, i.e. not a mass noun.
Not really. Using "any" would require changes to the original Finnish sentence. You should probably add a word that means any, and to drop or change the positive myös (also, in addition). Kind of you would not be asking anymore whether they also have some of this, but don't they have any of this either: Onko teillä myöskään yhtään/mitään pirtelöä? If there was no myös in the sentence, your question would be more valid.