Stop directly exposing hashmaps from Stan_math_signatures

[WardBrian]

This is a small change that tries to encapsulate more. In theory we could even use something other than a hash map now, including something that does computation (which could be one solution to #1373, though I'm not necessarily advocating for it)

Submission Checklist

• Run unit tests
• Documentation
  • If a user-facing facing change was made, the documentation PR is here:
  • OR, no user-facing changes were made

Release notes

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)

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 90.46%. Comparing base (1b601d5) to head (2f9392e).
Report is 6 commits behind head on master.

Additional details and impacted files

@@           Coverage Diff           @@
##           master    #1496   +/-   ##
=======================================
  Coverage   90.46%   90.46%           
=======================================
  Files          66       66           
  Lines       10707    10712    +5     
=======================================
+ Hits         9686     9691    +5     
  Misses       1021     1021           

Files with missing lines	Coverage Δ
src/analysis_and_optimization/Memory_patterns.ml	88.77% <100.00%> (ø)
src/frontend/Environment.ml	95.34% <100.00%> (ø)
src/frontend/Typechecker.ml	93.06% <100.00%> (+<0.01%)	⬆️
src/middle/Stan_math_signatures.ml	98.11% <100.00%> (+<0.01%)	⬆️
src/stan_math_backend/Lower_expr.ml	93.57% <100.00%> (+0.01%)	⬆️