And, there is no mention in the Siddur/Machzor of transferring sins to the animal or money. Is says ?? ??? ??, ?? ????? ??. And this Minhag, in one form or another is thousands of years old.
Tashlich is about invoking Hashem’s Middah of ?????? ??????? ?? ?? ??????. To ask why we Daven after doing that is like wondering why we fast in Yom Kippur after saying Slichos.