Avoid copying stiffness matrix for adjoint solves

We currently ask the stiffness matrix for its transpose, which allocates another sparse matrix. Now that we have a differentiable solver abstraction, we could have the adjoint solve use the action of the transpose, say using the MFEM `TransposeOperator`.

Start by tracing the differentiable solver abstraction and the code that asks the stiffness matrix for its transpose. Read MFEM's TransposeOperator usage and verify that adjoint solves apply the transpose action without allocating another sparse matrix; preserve the existing solve behavior.

Written by the indexing model from the issue text.