Document exported public API

[ChrisRackauckas-Claude]

Summary

This PR audits the exported public API and tightens the rendered documentation coverage. Please ignore this PR until reviewed by @ChrisRackauckas.

Changes:

• Adds rendered API coverage for the exported DEQs alias.
• Moves/expands the DeepEquilibriumNetwork docstring to the exported type definition point.
• Expands exported constructor/type docstrings with signatures, arguments, returns, and examples where appropriate.

Verification

Ran locally with Julia 1.10 using timeout 3600:

• timeout 3600 /home/crackauc/.juliaup/bin/julia +1.10 --project=@runic -e 'using Runic; exit(Runic.main(["--check", "."]))'\n - passed with exit code 0\n- Export audit one-liner over names(DeepEquilibriumNetworks; all=false)\n - exported=[:DEQs, :DeepEquilibriumNetwork, :DeepEquilibriumSolution, :MultiScaleDeepEquilibriumNetwork, :MultiScaleNeuralODE, :MultiScaleSkipDeepEquilibriumNetwork, :SkipDeepEquilibriumNetwork]\n - undocumented=Symbol[]\n - missing_api=Symbol[]\n- timeout 3600 /home/crackauc/.juliaup/bin/julia +1.10 --project=docs -e 'using Pkg; Pkg.develop(PackageSpec(path=pwd())); Pkg.instantiate(); include("docs/make.jl")'\n - passed with exit code 0\n - warnings observed: existing arXiv HTTP-to-HTTPS link redirects, existing large generated HTML warning for tutorials/basic_mnist_deq.md, and skipped deployment outside CI\n- timeout 3600 /home/crackauc/.juliaup/bin/julia +1.10 --project=. -e 'using Pkg; Pkg.test()'\n - passed\n - Utils Tests | 13 pass\n - Layers Tests | 1538 pass\n

[ChrisRackauckas-Claude]

Addressed the review on the DEQs handling.

Changes in the updated push:

• Removed the @doc ... DeepEquilibriumNetworks module-binding workaround from src/DeepEquilibriumNetworks.jl.
• Kept DEQs covered in rendered API docs as prose rather than adding a misleading source-site docstring for the module binding. A clean source docstring on const DEQs = DeepEquilibriumNetworks creates a module-valued binding that Documenter normalizes away during canonical missing-doc checks, which is why the previous workaround was noisy.
• Fixed the new SkipDeepEquilibriumNetwork doctest example to use a tuple-compatible Parallel(+, Dense, Dense) model; the previous bare Dense example caused the QA doctest failure on CI.
• Cleaned generated docs assets before commit.

Rerun locally with timeout 3600:

• Runic check: passed.
• Export/API audit: all exports appear in docs/src/api.md; all non-alias exported bindings have source doc metadata; DEQs is explicitly handled as the module alias exception in rendered API prose.
• Docs build (julia +1.10 --project=docs -e ... include("docs/make.jl")): passed with only existing link redirect / HTML size / skipped deployment warnings.
• QA + doctests on Julia 1.12 (julia +1.12 --project=test/qa -e ... include("test/qa/qa.jl")): passed, including doctests.

[ChrisRackauckas-Claude]

Follow-up after the review note: the branch now removes the module-level @doc ... DeepEquilibriumNetworks workaround entirely. DEQs is handled as a rendered API prose entry for the exported module alias, while the remaining exported user-facing API has source-site docstrings and @docs coverage. Generated docs assets were cleaned before the amended commit.\n\nRelevant local checks rerun after this update:\n- timeout 3600 julia +1.10 --project=@runic -e 'using Runic; exit(Runic.main(["--check", "."]))'\n- export/API audit script under julia +1.10 --project=.\n- timeout 3600 julia +1.10 --project=docs -e 'using Pkg; Pkg.instantiate(); include("docs/make.jl")'\n- timeout 3600 julia +1.12 --project=test/qa -e 'using Pkg; Pkg.instantiate(); include("test/qa/qa.jl")'\n\nThe PR GPU failure reproduces on main and is tracked separately in #222.