Document public code generation API

[ChrisRackauckas-Claude]

This PR should be ignored until reviewed by @ChrisRackauckas.

Summary

• declare CodegenFunctionOptions and codegen_function as public Symbolics API
• document codegen_function and render both low-level code-generation entries in the manual
• direct consumers to the owning public SymbolicUtils.IRStructure type rather than its Symbolics reexport
• test that both new public bindings retain docstrings
• bump Symbolics from 7.31.2 to 7.32.0 because this adds public API

Motivation

ModelingToolkit now uses these low-level code-generation entries, but Symbolics 7.31 introduced them without declaring them public. Publishing and documenting them at their owning package lets downstream code avoid relying on internals. The documentation also names SymbolicUtils.IRStructure through its owner module, where that type is declared public.

Local verification

• julia +1.12 --startup-file=no --project=. -e 'using Pkg; Pkg.instantiate(); using Test; include("test/codegen_function.jl")' — passed, including 9/9 CodegenFunctionOptions interface/public/documentation checks
• GROUP=Core julia +1.12 --startup-file=no --project=. -e 'using Pkg; Pkg.test(; allow_reresolve=true)' — passed (17,061 passed; 351 pre-existing broken checks), followed by 12/12, 12/12, and 14/14 passing SymbolicIndexingInterface testsets
• julia +1.12 --startup-file=no --project=docs -e 'using Pkg; Pkg.develop(path = pwd()); Pkg.instantiate(); include("docs/make.jl")' — passed; both low-level API entries and the SymbolicUtils.IRStructure owner qualification rendered without docstring or cross-reference warnings
• Runic 1.7 was checked across all 128 tracked Julia files; the existing repository is not Runic-clean across many unchanged files, while formatting each modified Julia range produced no changes
• git diff --check — passed

[codecov-commenter]

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Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 81.21%. Comparing base (45c0167) to head (ba50b0b).
⚠️ Report is 15 commits behind head on master.
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Additional details and impacted files

@@           Coverage Diff           @@
##           master    #1928   +/-   ##
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  Coverage   81.21%   81.21%           
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  Files          59       59           
  Lines        5807     5807           
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  Hits         4716     4716           
  Misses       1091     1091           

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[ChrisRackauckas-Claude]

Assertion follow-up and independent verification:

• Fresh pre-push audit: upstream master was 294457d1aaf130ca49bf38f2e161ba0886d422eb; the feature remote was 1d886fd717835e580eaf9add9036fa08f48c9359, containing the single documented commit by ChrisRackauckas-Claude. HEAD..upstream/master was empty. Commit 10ee6d52c411ee083ccb520a2a48e91797ceed4c was pushed as a normal fast-forward; no force push was used.
• Added two focused assertions that the public CodegenFunctionOptions and codegen_function bindings retain docstrings.
• Exact local Core command (Julia 1.12.6, isolated workspace depot): GROUP=Core timeout 3600 julia --startup-file=no --project=. -e 'using Pkg; Pkg.test(; allow_reresolve=true)'. Result: exit 0; 17,061 passed, 351 pre-existing broken, followed by 12/12, 12/12, and 14/14 passing SymbolicIndexingInterface testsets.
• Exact local docs command: timeout 3600 julia --startup-file=no --project=docs -e 'using Pkg; Pkg.develop(path = pwd()); Pkg.instantiate(); include("docs/make.jl")'. Result: exit 0; both new low-level API entries expanded without warnings. Existing warn-only diagnostics remain on unrelated pages.
• Runic 1.7 was run across all 128 tracked Julia files and reproduced existing repository-wide formatting differences. Runic output for the modified testset range was byte-identical to the source. git diff --check passed.
• All generated .audit and docs build artifacts were removed before committing; the commit contains only the two test assertions.

Benchmark check classification: its benchmark comparisons completed successfully with ratios effectively 1. The job failed only when peter-evans/create-or-update-comment received HTTP 403 Resource not accessible by integration while trying to post from the fork PR. This is a GitHub token-permission/infrastructure result, not a benchmark regression; no code or workflow change is warranted here.

[ChrisRackauckas-Claude]

Downstream follow-up: SciML/ModelingToolkit.jl#4744 raises the Symbolics floor to 7.32 and adds the ODEProblem code-generation regression. Local ModelingToolkitBase InterfaceI passed with 1,466 checks and 5 marked broken. Benchmark computations for this PR completed with ratios near 1 and identical allocations; the reported benchmark failure is only the AirspeedVelocity result-comment POST receiving 403 from fork-token permissions.

[ChrisRackauckas-Claude]

Owner-module follow-up (ba50b0b50d1e645caa7e1c6e27732fbacfa77759):

• Qualified every new public-doc reference to the IR type as SymbolicUtils.IRStructure, because SymbolicUtils declares/exports the type and Symbolics only reexports it.
• Targeted test/codegen_function.jl passed, including 9/9 interface/public/doc checks.
• The complete docs build passed; the owner-qualified prose and both new API entries produced no warning. Existing unrelated warn-only and external-link diagnostics remain elsewhere.
• Runic 1.7 was rerun over all 128 tracked Julia files (reproducing pre-existing repository formatting differences); Runic output for the modified Julia range was byte-identical.
• Before committing, generated .audit/docs artifacts were removed and git status contained only the two intended documentation files. Before pushing, upstream remained 294457d1aaf130ca49bf38f2e161ba0886d422eb and the feature remote remained exactly 10ee6d52c411ee083ccb520a2a48e91797ceed4c. The commit was pushed as a normal fast-forward; no force push was used.

The PR body now reflects the latest full Core totals (17,061 passed, 351 pre-existing broken), the 9/9 targeted result, and the owner qualification.

[ChrisRackauckas-Claude]

The refreshed benchmark check failed before running any Symbolics benchmark. AirspeedVelocity tried to download the ephemeral PR merge commit 775cdb7 as a repository revision, but that merge commit is not present in the clone, so Pkg reported Did not find rev ... in repository. The job never reached package benchmark execution. This is a benchmark-workflow checkout/revision failure, distinct from the earlier comment-permission failure and unrelated to the public-API/docs diff.