This PR should be ignored until reviewed by @ChrisRackauckas.

Summary

• Documents DiffEqGPU public/exported APIs in rendered docs, including reexported ensemble/callback APIs and package-owned algorithm constructors.
• Adds a developer-facing interfaces page for extension APIs used by solver/backend implementations.
• Moves interface docstrings to definition points and expands them with usage/interface rules and examples.
• Adds QA coverage checks that exported names have docstrings, exported names are declared in rendered docs, package-owned exports are in @docs, and developer extension points stay documented.

Audit

• Explicit export entries audited: 22
• public markers found in this repo: 0
• SciMLPublic/@public markers found in this repo: 0
• Missing source/original docstrings after this change: 0
• Missing rendered docs/API-page coverage after this change: 0

Validation

• timeout 3600 /home/crackauc/.juliaup/bin/julia +release --startup-file=no -e 'using Runic; for file in ARGS; Runic.format_file(file; inplace = true); end' docs/pages.jl src/DiffEqGPU.jl src/ensemblegpukernel/nlsolve/type.jl test/qa/qa.jl test/qa/public_api_docs.jl passed.
• timeout 3600 /home/crackauc/.juliaup/bin/julia +release --project=. --startup-file=no -e 'using DiffEqGPU; include("test/qa/public_api_docs.jl")' passed: public API docs coverage 1/1, rendered API docs coverage 3/3.
• timeout 3600 /home/crackauc/.juliaup/bin/julia +release --project=. --startup-file=no -e 'using Pkg; withenv("GROUP" => "QA") do; Pkg.test(); end' passed: Quality Assurance 22/22, JET static analysis 75/75.
• git diff --check passed.

Docs Build

I also ran the docs build against the local checkout with:

timeout 3600 /home/crackauc/.juliaup/bin/julia +release --project=docs --startup-file=no -e 'using Pkg; Pkg.develop(Pkg.PackageSpec(path=pwd())); Pkg.instantiate(); include("docs/make.jl")'

Documenter reached the final checks without :docs_block errors and failed only with [:example_block]. The observed example failures are pre-existing/external to this API-doc coverage patch:

• UndefVarError: islinear not defined in FunctionProperties while precompiling/loading SciMLSensitivity extensions.
• CUDA driver not functional in CUDA examples on this machine.
• UndefVarError: Rodas5 not defined in an existing tutorial example.
• A ModelingToolkit GPU example error: CuArray only supports element types that are allocated inline.

Process Notes

• Started from current origin/master and worked on a feature branch, not master.
• Did not skip, silence, or weaken tests/docs.
• PR branch is pushed from the ChrisRackauckas-Claude fork.