workroom; study; office (at home)
A room in a house or building used for work, such as a home office, study, or workshop.
My father is working late in his study.
This house has a spacious workroom.
仕事部屋 is a general term for any room used for work, while 書斎 specifically evokes a quiet space for reading, writing, or scholarly pursuits.
Compound of 仕事 (work) and 部屋 (room). The reading しごとべや follows standard rendaku voicing of へや to べや in compounds.