I went to AP in mid 2009 before the restoration (during the exterior painting and before the state halls opened).
They had none of what you pictured on display.
They had one outfit of each OTMA (I believe it was court dresses when they were very young), they also had a lot of Aleksey's toys and clothes, one doll and a few other trinkets of the girls', and Tatiana's regiment dress.
Probably now they have more considering the Children's Toy Exhibition, though I don't know that that will still be open next summer. Have a fun trip. It's a fantastic experience. Loved it so much I had to do it twice.