This will vary from apartment to apartment. Human ingenuity is a marvellous thing so I will not say it is impossible to practically re-use grey water but it sounds like a real challenge. Note that not all apartments are the same and water re-use may take unusual forms.
Greywater treatment/reuse system: inconspicuous & convenient near parking area.Cedar Springs Apartments is an affordable housing community with a goal to reduce potable water consumption through the treatment and reuse of greywater. Project Description.

As we can see from the illustration, High End Apartments With Grey Water Reuse has many fascinating aspects to explore.
Apartment dwellers, even in high-end estates like Kileleshwa, Kilimani, and Ruaka, often ration water a paradox in buildings marketed as fully serviced.Ideal (Global Standard). 24 hours. Public supply + greywater reuse. Why the Shortage Persists.

Can apartment buildings use greywater recycling systems? Apartment complexes are excellent candidates for greywater reuse because they generate large volumes of reusable water daily.
The acceptance rate of greywater reuse was higher, if consumers had more general knowledge and awareness of water treatment systems (Fielding et al., 2019). Demographics, particularly age, was found to be a significant determinant on the likelihood of accepting of greywater reuse.