Document public callback API examples

[ChrisRackauckas-Claude]

This draft PR should be ignored until reviewed by @ChrisRackauckas.

Summary

• Adds usage examples and return sections to user-facing public callback API docstrings.
• Moves remaining public constructor docs off @doc doc""" attachments and onto the definitions directly.
• Adds a QA test that every exported public name has a docstring and appears in a rendered @docs block.
• Removes the now-stale Markdown.@doc_str import.

Validation

• timeout 3600 /home/crackauc/.juliaup/bin/julia +release --project=test/qa -e 'using Pkg; Pkg.develop(PackageSpec(path=pwd())); Pkg.instantiate(); include("test/qa/qa.jl")' passed: Quality Assurance 17/17; Public API documentation coverage 3/3.\n- timeout 3600 /home/crackauc/.juliaup/bin/julia +release --project=. -e 'using Pkg; Pkg.test()' passed.\n- Runic v1.7.0 run with --inplace on touched Julia files.\n- git diff --check passed.\n\n## Docs Build Note\n- Full docs command timeout 3600 /home/crackauc/.juliaup/bin/julia +release --project=docs -e 'using Pkg; Pkg.develop(PackageSpec(path=pwd())); Pkg.instantiate(); include("docs/make.jl")' timed out after one hour during Documenter.HTMLWriter.render. Documenter had already completed ExpandTemplates, CrossReferences, and CheckDocument; the timeout stack was in HTML rendering/data-file hashing while rendering existing uncertainty plot assets. I am not marking full docs as passed.

[ChrisRackauckas-Claude]

CI note after opening this draft:

• tests / AD (julia 1, ubuntu-latest) failed before reaching DiffEqCallbacks assertions. The job fails while precompiling SciMLSensitivity, from SciMLBaseFunctionPropertiesExt with UndefVarError: islinear not defined in FunctionProperties. This looks like dependency resolution / upstream compatibility, not code touched by this PR.
• Local validation that completed before opening the PR remains:
  • QA: Quality Assurance 17/17; Public API documentation coverage 3/3.
  • Full local Pkg.test() passed.
  • Runic v1.7.0 --inplace on touched files.
  • Full docs build timed out after one hour during Documenter.HTMLWriter.render; see PR body for details.

I attempted to invoke the local AD group with Pkg.test(; test_args=["AD"]), but this repository invocation selected Core tests instead, so I stopped that duplicate run and am not counting it as validation.