Water is slippery but we lick our fingers to make them sticky to turn pages or open plastic bags, amirite?

Because that's saliva on our fingers not actual water.

Paper becomes more tactile when wet. So we are increasing the grip of the paper as it absolve a water.

And your fingertips become more grippy when you hydrate the skin...

It's because the moisture raises the adhesion of paper (and other items) to skin.