The reason your nails get softer after being in water and are easier to cut after taking a shower is the nails absorb in water just like your skin does when immersed in water.
Water will temporarily soften hardened keratin in your nails: calluses, cuticles, hair.
Which is why you should always soak your feet before buffing off calluses & cracked skin, clipping toenails, and soak your hands before gently pushing back your cuticles; also, why deep conditioner will more easily penetrate and then smooth the overlapping-shingle-like “cuticle” surface of your hair shaft while it’s wet).
Once enough time has passed and you’re thoroughly dried, your nails will harden back up to where they were before the shower.
Our nails are made of layers that make them strong and help them keep their shape.
One of the nails layers have keratin cells, which are special types of cells sort of like bone.
These Keratin cells are very thin and let water pass through to keep the nail hydrated and healthy.
If take a shower or go swimming for a while the nails get over loaded with water and become soft until it can be absorbed.