Refactor LCP solver architecture under dart::math::lcp

[jslee02]

Refactors the LCP solver implementation under dart::math::lcp.

• Introduces LcpSolver and LcpTypes abstractions for solver status, options, and results.
• Adds a pivoting LemkeSolver and reorganizes Dantzig sources under dart/math/lcp/dantzig, preserving the legacy install path.
• Updates constraints, benchmarks, and tests to the new headers and removes the deprecated namespace shim.
• Ignores generated stub output in docs/readthedocs.

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Before creating a pull request

• Run pixi run test-all to lint, build, and test your changes
• Add unit tests for new functionality
• Document new methods and classes (documentation split to Add LCP documentation #2240)
• Add Python bindings (dartpy) if applicable

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[jslee02]

@codex review

[chatgpt-codex-connector]

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[codecov]

Codecov Report

❌ Patch coverage is 9.09091% with 60 lines in your changes missing coverage. Please review.
✅ Project coverage is 60.95%. Comparing base (7160371) to head (b932316).

Files with missing lines	Patch %	Lines
dart/math/lcp/pivoting/LemkeSolver.cpp	0.00%	30 Missing ⚠️
dart/math/lcp/LcpTypes.cpp	0.00%	18 Missing ⚠️
dart/math/lcp/LcpSolver.cpp	0.00%	6 Missing ⚠️
dart/math/lcp/LcpTypes.hpp	0.00%	2 Missing ⚠️
dart/math/lcp/dantzig/Common.hpp	50.00%	2 Missing ⚠️
dart/math/lcp/LcpSolver.hpp	0.00%	1 Missing ⚠️
dart/math/lcp/pivoting/LemkeSolver.hpp	0.00%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #2241      +/-   ##
==========================================
- Coverage   61.05%   60.95%   -0.11%     
==========================================
  Files         353      359       +6     
  Lines       32144    32207      +63     
  Branches     4183     4187       +4     
==========================================
+ Hits        19627    19631       +4     
- Misses      12517    12576      +59     

Flag	Coverage Δ
unittests	60.95% <9.09%> (-0.11%)	⬇️

Flags with carried forward coverage won't be shown. Click here to find out more.

Files with missing lines	Coverage Δ
dart/constraint/BallJointConstraint.cpp	9.49% <ø> (ø)
dart/constraint/BoxedLcpConstraintSolver.cpp	53.70% <ø> (ø)
dart/constraint/ContactConstraint.cpp	76.62% <ø> (ø)
dart/constraint/DantzigBoxedLcpSolver.cpp	46.15% <ø> (ø)
dart/constraint/DantzigLCPSolver.cpp	0.00% <ø> (ø)
dart/constraint/JointConstraint.cpp	79.20% <ø> (ø)
dart/constraint/JointLimitConstraint.cpp	36.78% <ø> (ø)
dart/constraint/MimicMotorConstraint.cpp	77.24% <ø> (ø)
dart/constraint/PGSLCPSolver.cpp	0.00% <ø> (ø)
dart/constraint/PgsBoxedLcpSolver.cpp	71.42% <ø> (ø)
... and 18 more

... and 1 file with indirect coverage changes

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