Again. Same problem. You are fixated on the assumption that all randomness is chaotic.

Determining the outcome based on knowing the initial state ("all inputs") is the definition of chaotic.

Random means the outcome is not deterministic even when you have "all inputs". Also known as stochastic.

Chaotic = we lack information to predict.

Stochastic (random) = all information isn't enough to predict.

And you could hold the opinion that there is nothing really stochastic in the universe, that all randomness is really just chaotic and we just lack the ability to uncover it, which is ok, but again, there is no way you or anyone can prove that. To all ends and in all scientific fields, stochastic vs. chaotic is still taken as a very much real difference. If anyone could prove stochastic doesn't exist they would likely be the next world famous genius people would worship for centuries ahead.