After spending extended time in a bath, humans develop wrinkled skin. Is wrinkled skin the only effect of the immersion? Could a human spend extended time periods in water without causing some permanent damage? For sake of the question, let's say 7 days, or a month.
Wrinkling is an adaptative response of the skin, allowing for better grasp on objects when the skin is wet. The skin is a barrier of stacked cells mostly made of keratin and lipids. It is covered in aqueous and oily secretions (sweat, sebum) containing salts, acids, peptides, squalene, steroids, etc, as well as bacteria forming a biofilm and that defend you against pathogens.
If you are soaking continuously in water, these components are being washed away. One problem I immediately think of is fungal infection. Also, in warm water the skin is only semi-permeable, which is the basis of balneotherapy (absorbing minerals through the skin).
With time, water would disrupt the statum corneum, making the skin permeable, resulting in irritations, ulcerations, infections, loss of electrolytes, etc.
Look up "trench foot" or "immersion syndrome" , eg. How irritant is water? An overview. These disorders can leave permanent damage on the skin or the organs underneath. Stay dry.