Wiktionary
alt. (context idiomatic chiefly US English) Work or activity performed with the intention or result of occupying time, and not necessarily to accomplish something productive; routine work of low priority undertaken for the sake of avoiding idleness. n. (context idiomatic chiefly US English) Work or activity performed with the intention or result of occupying time, and not necessarily to accomplish something productive; routine work of low priority undertaken for the sake of avoiding idleness.
Wikipedia
Busy work (also referred to as make-work and busywork) can refer to activity that is undertaken to pass time and stay busy but in and of itself has no actual value. Busy work also occurs in business, military and other settings, in situations where people may be required to be present but may lack the opportunities, skills or need to do something more productive. People may engage in busy work to maintain an appearance of activity, in order to avoid criticism of being inactive or idle.
Usage examples of "busy work".
Wanting busy work, Laura moved to the shelves and began to tidy glassware.
But Maati was a messenger, not some kind of a subspecies to be ordered to do busy work because the viizaar felt like exercising her authority.
Wintrow had known it was busy work from the start, though why his father had wished to humiliate and irritate him, he could not fathom.
Now she saw it for what it was, a large, busy work area where servants came and went in haste while a cook reigned supreme.