A new dishwash soap was at your disposal in the kitchen and all daily needed stuff were available for you (there were soaps and shampoo in the shower...).
For the ustensils, you just used the one which were high in the shelves ( and here as a back up) but all ustensils you needed were under your hands and washed before your coming. I am leaving here and using it everyday.
For the baby things : there is a bed in the corner of the room, a baby bath that is embed near the toilets.
As the fact that the apartment seems to you small, unfortunately, parisian standards are not so high, and it is mentioned in the announce it is a two-rooms with a sofa-bed. I can say, the 35sq meters are well organised in here, without any wasted place.
I am sorry if you are not 100% satisfied with your experience.