> [the] spin is random and lives in a probability cloud that is probabilistic only until we observe it.

My mental model of it is kinda reversed. The maths assign a specific, deterministic state to each electron between each measurement. However, the "left" state is equal to "(up + down) / sqrt(2)". It then follows that when we measure an electron that is in the "left" state along the vertical direction, we get 50% up and 50% down: the probabilistic behavior happens when measuring, which "forces" an electron that was in the "left" state to become either "up" or "down".

I agree though that it would be less frustrating if there was some property of the electrons that would allow to predict in which state it'll collapse.