Steps for FVGQ gradients debugging

[jlperla]

• [ ] #114 lets us see if this use to work or has always been an issue. @wupeifan
• [x] Add H_p check to the symbolic gradient verificaiton. @jlperla
• [x] Add ȳ_p and x̄_p to the symbolic gradient verifciation. @jlperla
• [x] Drop the conditional in https://github.com/HighDimensionalEconLab/DifferentiableStateSpaceModels.jl/blob/main/src/generate_perturbation_derivatives.jl#L93-L101 and see if it helps to use H_p instead. @jlperla
• [x] Try to see if the buff itself has a bug.
  • Drop the whole of the buff. in the calculations inside https://github.com/HighDimensionalEconLab/DifferentiableStateSpaceModels.jl/blob/main/src/generate_perturbation_derivatives.jl#L85-L166 @jlperla
• [x] Try the old Sylvester solver instead of https://github.com/HighDimensionalEconLab/DifferentiableStateSpaceModels.jl/blob/main/src/generate_perturbation_derivatives.jl#L137 @wupeifan
• [x] Methodically go through the algebra for the preparation of the dH, R, E, C, A, etc. in https://github.com/HighDimensionalEconLab/DifferentiableStateSpaceModels.jl/blob/main/src/generate_perturbation_derivatives.jl#L110-L139 to look for typos relative to the algebra (e.g. a n_y or n_x mistake, a missing transpose, etc. that might not be relevant given sparsity pattern of RBC, etc.) @wupeifan

[wupeifan]

Basically the old Sylvester solver works. I think I've also find an issue in Michel's package which overwrites a bunch of input variables.