Quantum mechanics obviously provides a physical mechanism to implement free will. Whether this is the case is a different matter but the laws of physics don't rule it out.

It's not so obvious to me. The usual argument I've heard is that quantum randomness might sometimes be controlled by a non-physical entity external to our universe (in the sense of biasing measurements in critical moments). While an interesting fantastic idea, I don't think it brings much to the table, given that it is not testable. Is this what you meant or something else?

Otherwise, quantum mechanics at best leaves room for randomness (non-determinism, stochasticity) of the will, not what people usually mean when they say it.

If quantum randomness is controlled by a non-physical entity then it's just moving the goal posts. For me it's really simple. Free will is people not having a pre-destined path. If the non-determinism of quantum mechanics influences the way the lives of people change through their decisions this means there is free will. Everything else is really just pure philosophical drivel that can't be verified.

I agree. I just don't call this scenario free will, but nondeterminism, since it's less confusing. From my experience, when people talk about free will, they are not simply referring to nondeterminism.

Subjectively speaking, nondeterminism doesn't really seem to "buy" me anything. It does not restore any of the agency. In fact, if it is true, it gives me even more of a " arbitrary puppet" feeling than if the mind is deterministic.