Add method to get the factors of a Factorization (and maybe AbstractLinearOperator too)?

We have `LinearAlgebra.Factorization`, but I don't think we currently have a method to access the factors, e.g. a `factorsof(X::Factorization)::Tuple` or so.

This touches on JuliaLang/LinearAlgebra.jl#2 - it would be nice to eventually establish an abstract type for linear operators: We currently have [LinearMaps.jl](https://github.com/JuliaLinearAlgebra/LinearMaps.jl), [LinearOperators.jl](https://github.com/JuliaSmoothOptimizers/LinearOperators.jl), [SciMLOperators.jl](https://github.com/SciML/SciMLOperators.jl), but they don't share a common super type. So currently, code that wants to support arrays and linear operators in general has to use argument type `Any`, which isn't so nice in scenarios where you need to be a bit more precise with dispatch. And a lot of existing code that mainly relies on multiplication but requires `AbstractArray` could in principle be used on linear operators, but currently can't due to lack of a common supertype that might be agreeable to adopt.

Such an `AbstractLinearOperator` type could live in LinearAlgebra or a separate package, and there could be a `LinearOperatorLike = Union{AbstractLinearOperator, Factorization, AbstractMatrix}` that code can dispatch on instead of `Any`, but it would profit from a generic method to get the factors out of a `Factorization`.

CC @simonbyrne, @timholy, @ChrisRackauckas, @dkarrasch, @Jutho, @dpo, @abelsiqueira who might be interested (and will probably have an opinion on) this.

Start by reviewing the existing LinearAlgebra.Factorization API and the linked JuliaLang/LinearAlgebra.jl#2 discussion. Determine whether the requested factor-access method belongs in LinearAlgebra and how it should interact with a possible AbstractLinearOperator design; done means an agreed API and corresponding implementation scope.

Written by the indexing model from the issue text.