Speaking as a physicist, I think you're basically on the right track! (But also, this is as much philosophy of math/science as it is physics, so I wouldn't quite call myself an authority on this.)
I definitely think of probability as something like a mental framework with a set of axioms that can be applied to anything where the axioms fit well enough, which can be "true" quantum probability or sequential frequentist dice rolls or subjective Bayesian stuff.
I definitely think of probability as something like a mental framework with a set of axioms that can be applied to anything where the axioms fit well enough, which can be "true" quantum probability or sequential frequentist dice rolls or subjective Bayesian stuff.