Remove 'Base' as a dependency

[WardBrian]

See #1655

This is the ultimate conclusion of the patch sequence #1643 #1644 #1650 #1652.

After updating to 5.5, Base was providing us (up to renaming) essentially just:

• Polymorphic sets
• Hash sets
• A few small quality of life functions

These are all easy to provide ourselves, which means we can remove the dependency entirely.

The binaries produced with dune build --profile release from this branch are 12mb, down from 15mb on master. Shockingly, they're also the same speed if not faster (especially when running optimizations):

Summary
  ./stanc-nobase ./test/integration/good/code-gen/mother.stan ran
    1.03 ± 0.07 times faster than ./stanc-master ./test/integration/good/code-gen/mother.stan

Summary
  ./stanc-nobase --O1 ./test/integration/good/compiler-optimizations/copy_fail.stan ran
    1.56 ± 0.10 times faster than ./stanc-master --O1 ./test/integration/good/compiler-optimizations/copy_fail.stan

Summary
  ./stanc-nobase --Oexperimental ./test/integration/good/compiler-optimizations/copy_fail.stan ran
    2.03 ± 0.16 times faster than ./stanc-master --Oexperimental ./test/integration/good/compiler-optimizations/copy_fail.stan

Javascript builds are down to 16mb from 19mb, with minified sizes roughly the
same.

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

Decreased our dependence on third-party libraries.

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)

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[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 92.26%. Comparing base (9d7b62a) to head (096bed4).

Additional details and impacted files

@@              Coverage Diff               @@
##           std/middle    #1663      +/-   ##
==============================================
+ Coverage       92.13%   92.26%   +0.13%     
==============================================
  Files              70       69       -1     
  Lines           10140    10124      -16     
==============================================
- Hits             9342     9341       -1     
+ Misses            798      783      -15     

Files with missing lines	Coverage Δ
src/middle/UnsizedType.ml	84.57% <100.00%> (ø)
src/stan_math_backend/Cpp.ml	90.90% <100.00%> (ø)
src/stan_math_backend/Transform_Mir.ml	95.55% <100.00%> (+<0.01%)	⬆️

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