Final answer:
The governess longs to engage in domestic tasks and child care to feel needed, but her automated house has made these tasks obsolete, causing her existential distress.
Step-by-step explanation:
The governess longs to perform domestic duties such as mending socks, cleaning the house, and being actively involved in the care of the children, but she cannot bring herself to do these because the automated house has taken over all these tasks, making her feel unnecessary and obsolete.
This theme is echoed across various works of literature where characters struggle with feelings of purposelessness or the desire to feel needed, whether it is in the face of technological advancements or social expectations.