Mathlib torsion-free abelian groups: assume [HasUniqueDiv G], not IsAddTorsionFree

Mathlib (v4.35.0, v4.36.0-rc2) has three overlapping classes: IsAddTorsionFree, HasUniqueDiv (added with the 2026-09-29 deprecations; nsmul_right_injective) and Module.IsTorsionFree ℤ G. For an AddCommGroup G, inferInstance from [HasUniqueDiv G] gives IsAddTorsionFree G, Module.IsTorsionFree ℤ G, NoZeroSMulDivisors ℤ G, and HasUniqueDiv / Module.IsTorsionFree ℤ for any AddSubgroup.closure or AddSubgroup. None of these work in the other direction. [Module.IsTorsionFree ℤ G] and [IsAddTorsionFree G] do not give HasUniqueDiv G, they do not give each other, and neither gives Module.IsTorsionFree ℤ on a subgroup, where you need Subtype.val_injective.moduleIsTorsionFree _ fun _ _ ↦ rfl. If you are handed IsAddTorsionFree on a commutative group, convert once: (hasUniqueDiv_iff G).2 fun n hn a b h => IsAddTorsionFree.eq_of_nsmul_eq_nsmul_of_addCommute hn (AddCommute.all a b) h. ℤ, ℝ and Fin 3 → ℚ have HasUniqueDiv instances.