Add native spherical harmonic surface coordinates to coupled equilibrium

CMakeLists.txt

@@ -77,6 +77,8 @@ target_sources(mean_field
         libmeanfield/impl/mapping/domain_mapper.cpp
         libmeanfield/impl/mapping/transformations.cpp
         libmeanfield/impl/deformation/nodal_radial_surface.cpp
+        libmeanfield/impl/deformation/spherical_harmonic_surface.cpp
+        libmeanfield/impl/deformation/surface_metric.cpp
         libmeanfield/impl/deformation/radial_extensions.cpp
         libmeanfield/impl/deformation/safe_newton_step.cpp
         libmeanfield/impl/operators/gravity_field.cpp
@@ -231,10 +233,12 @@ target_sources(mean_field
         libmeanfield/interface/deformation/descriptors.cppm
         libmeanfield/interface/deformation/surface_prescription.cppm
         libmeanfield/interface/deformation/nodal_radial_surface.cppm
+        libmeanfield/interface/deformation/spherical_harmonic_surface.cppm
         libmeanfield/interface/deformation/interior_extension.cppm
         libmeanfield/interface/deformation/vacuum_extension.cppm
         libmeanfield/interface/deformation/radial_extensions.cppm
         libmeanfield/interface/deformation/domain_deformation.cppm
+        libmeanfield/interface/deformation/surface_metric.cppm
         libmeanfield/interface/deformation/safe_newton_step.cppm
         libmeanfield/interface/models/stellar_model.cppm
         libmeanfield/interface/operators/root_manifest.cppm
@@ -344,12 +348,14 @@ add_executable(tests
         tests/deformation/contracts.cpp
         tests/deformation/surface_scalar_dof_map.cpp
         tests/deformation/nodal_radial_surface.cpp
+        tests/deformation/spherical_harmonic_surface.cpp
         tests/deformation/radial_extensions.cpp
         tests/deformation/domain_deformation.cpp
         tests/deformation/safe_newton_step.cpp
         tests/operators/prepared_mass_normalization.cpp
         tests/operators/prepared_angular_momentum.cpp
         tests/operators/prepared_stellar_equilibrium.cpp
+        tests/operators/spherical_harmonic_equilibrium.cpp
         tests/utils/domain.cpp
         tests/field/field_base.cpp
         tests/field/field_registry.cpp
@@ -359,6 +365,7 @@ add_executable(tests
         tests/preconditioning/backends.cpp
         tests/preconditioning/gravity_field.cpp
         tests/preconditioning/material_surface.cpp
+        tests/preconditioning/spherical_harmonic_surface.cpp
         tests/preconditioning/stellar_structure.cpp
         tests/preconditioning/specification_border.cpp
         tests/extensions/fixed_magnetic_specific_energy.cpp
@@ -367,6 +374,7 @@ add_executable(tests
         tests/normalization/plan.cpp
         tests/normalization/physical_riesz.cpp
         tests/normalization/stellar_equilibrium.cpp
+        tests/normalization/spherical_harmonic_surface.cpp
         tests/user-api/stellar_equilibrium.cpp
         tests/solver/preconditioning_diagnostics.cpp
         tests/solver/stellar_equilibrium_architecture.cpp