Compiler support for laplace_latent_solve(_tol)

[florence-bockting]

Submission Checklist

This PR refers to math PR#337 in which we implemented laplace_latent_solve and laplace_latent_solve_tol.

• Run unit tests
• Documentation
  • If a user-facing facing change was made, the documentation PR is here: Document laplace_latent_solve(_tol) docs#968
  • OR, no user-facing changes were made

Release notes

• Adds Stan compiler support for Math’s laplace_latent_solve(_tol), which return tuple(vector, matrix) (posterior mean and Cholesky factor).

Copyright and Licensing

By submitting this pull request, the copyright holder is agreeing to
license the submitted work under the BSD 3-clause license (https://opensource.org/licenses/BSD-3-Clause)

This PR used AI assistance (Cursor).

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 91.51%. Comparing base (5496e41) to head (ec9a2f8).

Additional details and impacted files

@@           Coverage Diff           @@
##           master    #1649   +/-   ##
=======================================
  Coverage   91.51%   91.51%           
=======================================
  Files          67       67           
  Lines        9977     9979    +2     
=======================================
+ Hits         9130     9132    +2     
  Misses        847      847           

Files with missing lines	Coverage Δ
src/frontend/Typechecker.ml	94.88% <100.00%> (+<0.01%)	⬆️
src/stan_math_signatures/Stan_math_signatures.ml	86.27% <ø> (ø)

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