But how much chakra does shunshin even take up? It shouldn't even use a significant amount, for it to be held back in base.Releasing more chakra will generally make one faster of course there are different factors such as training and chakra potency. Itachi is more suited for higher speed combat due to his Sharingan and has unparalleled Chakra due to being an Uchiha, so it makes sense why he would be faster.
But when comparing two individuals with the same training, same genetics, and same chakra potency, the one who releases more chakra is going to be faster. In this case, comparing Byakugou Tsunade and Base Tsunade, the only difference is the amount of chakra Byakugou Tsunade releases which is why she should be faster.
This whole "she has more chakra so she is faster" all assumes that it takes up a lot of chakra or something to use a simple shunshin.