if we add true randomness to an input-based decision, it stops being predetermined, but there’s still a logically conclusive choice you’re going to make, based on the incomplete inputs you have. You cannot ‘freely’ decide to not pick that choice

I think you are contradicting yourself. If you cannot freely choose something else, then your choice is predetermined.

Whereas if a choice stops being predetermined, then there is no “logically conclusive choice” that you are definitely going to make. There is a range of possible choices, one of them is chosen by you, and the others could have been chosen but weren’t.