Clean up embeddedmesh implementation

[eulovi]

Description and Context

One problem that I noticed in the PR #1613 is that the current embeddedmesh implementation in constraint_framework is not flexible enough to add new coupling strategies. So far, only the Mortar method is implemented. Therefore, in this PR a base class SolidToSolidCouplingManager is introduced. This class can work as a base class for other methods and holds basic functionality needed for embedded mesh strategies. Also I tried to clean how parameters are obtained, so that no unnecessary parameters are called if the coupling strategy doesn't require them.

Related Issues and Pull Requests

Related to #1613

[maxfirmbach]

Overall looks nice 👍. I have left some comments 😃.

[Copilot]

Pull request overview

Refactors the embedded-mesh constraint implementation in constraint_framework to make it extensible beyond the Mortar method by introducing a common SolidToSolidCouplingManager base and routing evaluation/output through a selected coupling strategy.

Changes:

• Introduces SolidToSolidCouplingManager base class and moves shared embedded-mesh setup/cut/output-integration-point logic into it.
• Updates EmbeddedMeshConstraintManager to construct and use a strategy-specific coupling manager (currently Mortar).
• Adapts SolidToSolidMortarManager to inherit from the new base and override the strategy-specific assembly/output/energy pieces.

Reviewed changes

Copilot reviewed 6 out of 6 changed files in this pull request and generated 9 comments.

Show a summary per file

File	Description
src/constraint_framework/4C_constraint_framework_submodelevaluator_embeddedmesh.hpp	Switches embedded-mesh submodel evaluator to a coupling-strategy-based manager interface.
src/constraint_framework/4C_constraint_framework_submodelevaluator_embeddedmesh.cpp	Implements parameter extraction and coupling-manager factory logic; routes evaluation/output/energy through the manager.
src/constraint_framework/4C_constraint_framework_embeddedmesh_solid_to_solid_mortar_manager.hpp	Makes Mortar manager derive from SolidToSolidCouplingManager and overrides the base interface.
src/constraint_framework/4C_constraint_framework_embeddedmesh_solid_to_solid_mortar_manager.cpp	Adjusts Mortar manager construction/setup and renames the force/stiffness contribution API to match the base.
src/constraint_framework/4C_constraint_framework_embeddedmesh_solid_to_solid_coupling_manager.hpp	Adds the new common base class API/state shared by embedded-mesh coupling managers.
src/constraint_framework/4C_constraint_framework_embeddedmesh_solid_to_solid_coupling_manager.cpp	Implements shared cut/setup, visualization registration, and helper utilities for coupling managers.

[eulovi]

Thanks for your comments @maxfirmbach @isteinbrecher (and sorry for taking so long to resolve this)!