It is actually a good habit to put a washbasin and towel next to the office door. We can see from ancient social phenomena. For example, after the ancient emperor got up, some ladies-in-waiting immediately washed their faces with some mouthwash to do a good job of cleaning and hygiene for the emperor. So later officials learned this good habit and carried it forward well. This phenomenon has always existed in contemporary society, but compared with these ancient dignitaries, it is not so exaggerated.
In fact, this phenomenon has a tendency to spread and expand in contemporary society. For example, in some doctors' offices, there are often some washbasins, which are equivalent to this ancient washbasin. Not only can you clean your hands in the washbasin, but you can also be cold-faced when you are sleepy and let your mind recover.
So to sum up, putting washbasins and towels next to the door of the office is mainly for the convenience of cleaning and hygiene, so that you can have a mood of going to work. As for the cause of Feng Shui, it is subjective and has no scientific basis.