Vectorize equilibrium derivatives and reuse Jacobian factorization

[markleader]

Summary

Reformulate equilibrium derivative post-processing as a vector-valued response Jacobian and reduce direct-method solve cost by reusing one Jacobian factorization for all sensitivity right-hand sides.

Changes

• Add explicit input mapping from [state1, state2, w0] to the residual inputs.
• Assemble derivatives for temperature, mixture/species amounts, and thermodynamic properties in a response Jacobian.
• Solve the direct sensitivity system as a multiple-right-hand-side system.
• Preserve the existing public derivative fields by unpacking the response Jacobian.
• Add coverage for the block linear solve and response-matrix mapping.

Testing

• ctest --test-dir build-dev -R cea_core_test --output-on-failure (118 tests passed)

Compatibility / Numerical behavior

• No expected changes to numerical results
• Expected changes (explain and provide validation)

The public derivative interface and scientific behavior are preserved; only the internal formulation and solve strategy have changed.