In relation to other comments here and here I think we should re-add support for getproperty(::Tangent{<:Cholesky}, ...) with :U or :L along with :factors. This would make release 1.35.3 slightly less breaking.
https://github.com/invenia/Nabla.jl/pull/217/files#diff-a51816a450e57348c1c90d807b0a793092bb7e368d759102888820eb2e0ee025R55