Cavity insulation of intermediate ceiling

I am in the middle of renovating our single-family house. The roof is supposed to get a completely new insulation, even though I do not want to use the attic as living space. In the ceiling between the first floor and the attic, there is a continuous cavity filled with a white insulation material unknown to me. I want to remove all the old stuff and now wonder whether I have to insulate the floor between the stories again afterwards, or if it is sufficient to properly insulate only the roof?

You do not need to insulate the floor ceiling; the insulation of the roof surfaces is sufficient. Since the mentioned ceiling is then located inside the insulated building envelope, cavity insulation would also be unnecessary.