> In classical physics, the universe is deterministic: every action is a necessary consequence of what happened before. In this view, our actions are predetermined too.

Sure, but the deterministic chaos [1] arising within classical physics says that any predetermined actions depend on upon effectively unknowable aspects of initial conditions. Nothing probabilistic required.

Easiest example is anything dependent on turbulent fluids, which are found everywhere in the atmosphere and the oceans. Another place with turbulence is the human heart [2]. There's deterministic chaos lurking behind the oxygenation of every cell in your body.

Predetermined actions from a chaotic system are indistinguishable from free will. Occam's Razor suggests free will, being simpler and just as predictive, is the better model for human behavior.

Just because it's fun: Why is the universe like this? The anthropic principle [3]! Without fluid turbulence the other available diffusion mechanisms are too slow to evolve creatures like us. Literally, either turbulence is a classical physics PITA or you don't exist [4].

[1] https://en.wikipedia.org/wiki/Chaos_theory

[2] https://cvphysiology.com/hemodynamics/h007

[3] https://en.wikipedia.org/wiki/Anthropic_principle

[4] Things one observes when procrastinating on a turbulence-related dissertation.