#481 possibly broke `ishermitian`

After #481 , ishermitian is now broken (maybe other methods too?) when working with ForwardDiff.Dual.

julia> Pkg.status()
Status `/tmp/jl_gs3tnK/Project.toml`
  [f6369f11] ForwardDiff v0.10.33
  [37e2e46d] LinearAlgebra

julia> using LinearAlgebra, ForwardDiff

julia> x = [1 0.5; 0.5 1]
2×2 Matrix{Float64}:
 1.0  0.5
 0.5  1.0

julia> ishermitian(x)
true

julia> f(x) = sum(cholesky(reshape(x, 2, 2)))
f (generic function with 1 method)

julia> ForwardDiff.gradient(vec(x))
ERROR: MethodError: no method matching gradient(::Vector{Float64})
Closest candidates are:
  gradient(::Any, ::StaticArraysCore.StaticArray) at ~/.julia/packages/ForwardDiff/eqMFf/src/gradient.jl:44
  gradient(::Any, ::StaticArraysCore.StaticArray, ::ForwardDiff.GradientConfig) at ~/.julia/packages/ForwardDiff/eqMFf/src/gradient.jl:45
  gradient(::Any, ::StaticArraysCore.StaticArray, ::ForwardDiff.GradientConfig, ::Val) at ~/.julia/packages/ForwardDiff/eqMFf/src/gradient.jl:46
  ...
Stacktrace:
 [1] top-level scope
   @ REPL[10]:1

julia> ForwardDiff.gradient(f, vec(x))
ERROR: PosDefException: matrix is not Hermitian; Cholesky factorization failed.
Stacktrace:
  [1] checkpositivedefinite(info::Int64)
    @ LinearAlgebra /opt/julia-1.8.2/share/julia/stdlib/v1.8/LinearAlgebra/src/factorization.jl:18
  [2] cholesky!(A::Matrix{ForwardDiff.Dual{ForwardDiff.Tag{typeof(f), Float64}, Float64, 4}}, ::NoPivot; check::Bool)
    @ LinearAlgebra /opt/julia-1.8.2/share/julia/stdlib/v1.8/LinearAlgebra/src/cholesky.jl:299
  [3] #cholesky#162
    @ /opt/julia-1.8.2/share/julia/stdlib/v1.8/LinearAlgebra/src/cholesky.jl:402 [inlined]
  [4] cholesky (repeats 2 times)
    @ /opt/julia-1.8.2/share/julia/stdlib/v1.8/LinearAlgebra/src/cholesky.jl:402 [inlined]
  [5] f(x::Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(f), Float64}, Float64, 4}})
    @ Main ./REPL[9]:1
  [6] vector_mode_dual_eval!
    @ ~/.julia/packages/ForwardDiff/eqMFf/src/apiutils.jl:37 [inlined]
  [7] vector_mode_gradient(f::typeof(f), x::Vector{Float64}, cfg::ForwardDiff.GradientConfig{ForwardDiff.Tag{typeof(f), Float64}, Float64, 4, Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(f), Float64}, Float64, 4}}})
    @ ForwardDiff ~/.julia/packages/ForwardDiff/eqMFf/src/gradient.jl:106
  [8] gradient(f::Function, x::Vector{Float64}, cfg::ForwardDiff.GradientConfig{ForwardDiff.Tag{typeof(f), Float64}, Float64, 4, Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(f), Float64}, Float64, 4}}}, ::Val{true})
    @ ForwardDiff ~/.julia/packages/ForwardDiff/eqMFf/src/gradient.jl:19
  [9] gradient(f::Function, x::Vector{Float64}, cfg::ForwardDiff.GradientConfig{ForwardDiff.Tag{typeof(f), Float64}, Float64, 4, Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(f), Float64}, Float64, 4}}}) (repeats 2 times)
    @ ForwardDiff ~/.julia/packages/ForwardDiff/eqMFf/src/gradient.jl:17
 [10] top-level scope
    @ REPL[11]:1

This is because now the A[i,j] != adjoint(A[j,i]) check performed in ishermitian returns true.

Reproduce the failure from the issue, then read the ishermitian-related logic implicated by the A[i,j] != adjoint(A[j,i]) check and the LinearAlgebra cholesky.jl stack frame. Compare behavior for ordinary values and ForwardDiff.Dual values, including whether other affected methods reproduce it. Done means the reported cholesky path no longer rejects the Hermitian Dual matrix and regression coverage protects the behavior.