Actually, toes and fingers don’t wrinkle in the bathtub at all.
They are puckering from swelling. The thick outside layer of skin called the stratum corneum takes on excess water when soaked, sort of like dried beans when soaked in water.
The underlying skin and connective tissue don’t absorb water and don’t swell along with it.
This anchoring of the skin-tissue layers makes the swelled area appear puckered.
It’s not just the fingers and toes that do this, though they are easier to see because the stratum corneum in those areas is thickest.
When you see your fingers and toes wrinkling, take it as a sign that your entire body is on guard to prevent water, soap, dirt, and germs from invading through your skin.