Document public Integrals APIs

[ChrisRackauckas-Claude]

Summary

This PR documents the Integrals-owned public API surface and adds a QA guard that requires exported public bindings to have both source docstrings and rendered docs entries.

Please ignore this PR until it has been reviewed by @ChrisRackauckas.

Changes

• Adds/expands source docstrings for public Integrals algorithms, wrappers, transformation helpers, sampled-data algorithms, and solve entry points.
• Adds missing public API entries to the rendered docs.
• Adds a focused QA test that audits Integrals-owned exported names for docstrings and @docs coverage.

Validation

• git diff --check origin/master...HEAD
• julia +release --startup-file=no --project=. -e 'using Pkg; Pkg.instantiate(); using Runic; exit(Runic.main(["--check", "."]))'
• julia +release --startup-file=no --project=docs -e 'using Pkg; Pkg.develop(PackageSpec(path=pwd())); Pkg.instantiate(); include("docs/make.jl")'
• GROUP=QA julia +release --startup-file=no --project=. -e 'using Pkg; Pkg.instantiate(); Pkg.test()'
• GROUP=Core julia +release --startup-file=no --project=. -e 'using Pkg; Pkg.instantiate(); Pkg.test()'
• julia +1.10 --startup-file=no --project=test/AD -e 'using Pkg; Pkg.develop(PackageSpec(path=pwd())); Pkg.instantiate(); include("test/AD/derivative_tests.jl"); include("test/AD/nested_ad_tests.jl")'

The root Pkg.test() on Julia release was also attempted first, but it timed out in the AD group because the root test harness runs all groups; test/test_groups.toml only runs AD on LTS, so the final validation above uses the CI-aligned groups/channels.