Enable NeuralPDE rendered public API docs QA

[ChrisRackauckas-Claude]

Ignore this PR until reviewed by @ChrisRackauckas.

Summary

• Enables rendered public API documentation checking in NeuralPDE QA.
• Uses the existing dynamic REEXPORTED_API set for both source-docstring and rendered-docs ignores, so dependency-owned reexports stay owned by their source packages.
• Removes the stale hard-coded upstream ignore list from the QA config.

Validation

• git diff --check
• julia +1.10 --project=/home/crackauc/sandbox/tmp_20260708_051717_3275/toolenvs/runic -e 'using Runic; exit(Runic.main(ARGS))' -- --check test/qa/qa.jl\n- julia +1.10 --project=tmp/neuralpde_qa_env -e 'using Pkg; Pkg.develop(Pkg.PackageSpec(path=pwd())); Pkg.instantiate(); include("test/qa/qa.jl")' (Quality Assurance | 14 pass, 1 broken, 15 total)\n

[ChrisRackauckas-Claude]

CI triage as of 2026-07-17 03:01 UTC for head 08f42378e11be42f5d93b80eafdfc091523ccb15:

Docs/rendered public API scope is green:

• tests / QA (julia 1, ubuntu-latest) passed in CI: https://github.com/SciML/NeuralPDE.jl/actions/runs/29549281275/job/87788241500
• Local validation passed with Julia 1.10: GROUP=QA timeout 3600 /home/crackauc/.juliaup/bin/julia +1.10 --project=. -e 'using Pkg; Pkg.test()'
  • summary: QA/qa.jl | 14 pass, 1 broken, 15 total; Testing NeuralPDE tests passed
• Documentation is skipped by the workflow on this PR, not failing.

No docs/docstrings/rendered-public-API fix is needed, so I made no code changes and did not push a commit.

Out-of-scope failures observed:

• AdaptiveLoss on both Julia 1.11 and lts fails in test/AdaptiveLoss/adaptive_loss__2d_poisson_gradientscaleadaptiveloss.jl on total_diff_rel < 0.4, with evaluated values around 0.6431 at line 96 and 0.5202 at line 102. This is a behavioral AdaptiveLoss failure and outside this PR's docs/QA scope.
• PDESystemLibrary.jl/NeuralPDE downstream fails before downstream tests run: SciMLTesting folder mode gets GROUP="NeuralPDE", but that downstream checkout declares only Core and QA groups, so run_tests errors with GROUP="NeuralPDE" is not ... declared in test_groups.toml. This is downstream/group-routing, not rendered API docs QA.

Several non-QA behavioral jobs were still pending when checked; I did not modify them under this scope.