Cheesecake Birthday Poke Cake

[16.25] oz box of butter cake mix (plus ingredients to prepare)

[3.4] oz boxes instant cheesecake pudding mix

cold whole milk

[8] oz cream cheese (softened)

powdered sugar

pure vanilla extract

frozen whipped topping (thawed or 4 cups sweetened fresh whipped cream)

[15.25] oz package Golden Birthday Cake Oreo cookies (chopped and divided)

sprinkles