Melete234, there’s a pretty important difference between paper and a paper in this sentence.
The former is an uncountable amount...there’s no unit of measure associated with the word “paper” in your phrase. It could be referring to some amount of notebook paper, or even a truckload of rolls of paper (like that used in printing newspapers).
The latter example (the one in the Duo question) is a countable quantity. The phrase “a paper” implies that there’s a known unit of measure being asked about, such as a single page.
...I'm not sure I'm following you.
I get the distinction you draw between 'countable' and 'uncountable'; but as far as I can tell, 'páipéar' can be used for either of the two, and therefore there is no way to say that the use of 'páipéar' in this sentence falls into the first or second category.