There's boondoggle and busywork.
Answer from Matt Eckert on Stack ExchangeHow is the word 'futile' different from other adjectives like it?
The words fruitless and vain are common synonyms of futile. While all three words mean "producing no result," futile may connote completeness of failure or unwisdom of undertaking.
// resistance had proved so futile that surrender was the only choice left
How do 'fruitless' and 'vain' relate to one another, in the sense of 'futile'?
Fruitless comes close to vain but often suggests long and arduous effort or severe disappointment.
// fruitless efforts to obtain a lasting peace
When could 'vain' be used to replace 'futile'?
The words vain and futile can be used in similar contexts, but vain usually implies simple failure to achieve a desired result.
// a vain attempt to get the car started
Hi English speakers! Just out of curiosity, is there any idiom in English related to the myth of Sisyphus? More specifically, some term that you'd use to describe pointless or repetitive duty?