The simple meaning of ביתו is the same as the way the tanna refers to his clothes as מכבדותא in the list of things that he called by their purpose – not that the clothes are kavod thensleves, but that they honor the one who wears them… Referring to his wife as beisa was because she was the akerew habayis.
Your interpretation is in the realm of drush, that not only is she the homemaker, but she is the “home” of the family