What is the ruling on showing little care for one's parents due to being preoccupied with studies, even while living with them and having siblings and nephews/nieces to attend to their needs? Is this considered a sin?

There is no harm in being preoccupied with studies rather than serving one's parents if they are not in need. However, it is preferable to allocate time to sit with them and check on their well-being. It is obligatory to answer them if they call, especially if what you are learning is not an individual obligation (fard ‘ayn) or if you do not fear missing out on it. The proof for this is that answering them takes precedence over supererogatory prayers, as in the story of Jurayj, where the correct action for him was to answer his mother because his prayer was supererogatory while honoring her was obligatory.