No stir plate for dry yeast.
Hydrating is just that, adding sterilized room temp water to plump up the yeast.
Proofing is water and some fermentable sugar that will start the yeast working, thus "proof" the yeast is good.
A stir plate is used when you want to grow more yeast than you have. Maybe from a bottle harvest, a slant, or a vile of liquid yeast. Liquid yeast doesn't last nearly as long as dry, and will start to die off. A stir plate allows you to grow a little or a lot depending on the beer your brewing.
I don't use dry yeast too often, but many (myself included) just dump the package in and put the lid on.