`cholesky` of a Symmetric KeyedArray strips out the Symmetric

Hello, I got tripped up by this:

julia> X = Symmetric(KeyedArray([1.0 0.1; 0.2 1.0], ([:a, :b], [:a, :b])))
2×2 Symmetric{Float64, KeyedArray{Float64, 2, Matrix{Float64}, Tuple{Vector{Symbol}, Vector{Symbol}}}}:
 1.0  0.1
 0.1  1.0

julia> isposdef(X) # Doesn't give expected answer
false

julia> isposdef(collect(X)) # Gives expected answer
true

Note that

julia> X = Symmetric([1.0 0.1; 0.2 1.0])
2×2 Symmetric{Float64, Matrix{Float64}}:
 1.0  0.1
 0.1  1.0

julia> isposdef(X) # Gives expected answer
true

As far as I can tell, this is because we reach this method in this package:

LinearAlgebra.cholesky(A::Hermitian{T, <:KeyedArray{T}}; kwargs...) where {T} =
    cholesky(parent(A); kwargs...)

And

julia> parent(Hermitian(X))
2-dimensional KeyedArray(...) with keys:
↓   2-element Vector{Symbol}
→   2-element Vector{Symbol}
And data, 2×2 Matrix{Float64}:
        (:a)  (:b)
  (:a)   1.0   0.1
  (:b)   0.2   1.0

which does not satisfy isposdef since it's not Hermitian.

This is with AxisKeys v0.1.22 and julia v1.6.0

Reproduce the Julia examples in the issue, then locate the LinearAlgebra.cholesky method for Hermitian values containing KeyedArray data. Compare its behavior with Symmetric and collect(X), and determine how the reported wrapper or symmetry information is lost. Done means the keyed symmetric case gives the expected positive-definiteness result without breaking the existing method behavior.