[xelxebar]

> Doesn’t quantum mechanics leave open the possibility that our universe is fundamentally probabilistic?

Not really. A wave function propogates in a perfectly deterministic manner. There's not anything probabilistic baked into QM.

Probability comes in at what's called the Measurement Problem. Right now, we ad hoc apply the Born rule to project complex amplitudes into probability distributions whenever convenient, but there's actually no good understanding of why the Born rule works at all. It's just sorta tacked onto QM at this point.