Use rendered public API docs QA

[ChrisRackauckas-Claude]

Ignore this PR until reviewed by @ChrisRackauckas.

Summary

• Enable SciMLTesting rendered public API docs QA across Optimization.jl QA groups with api_docs_kwargs = (; rendered = true, ...).
• Add a shared helper that computes rendered_ignore only for dependency-owned reexports not rendered in the Optimization docs.
• Render the package-owned OptimizationBase module and add its source module docstring.

Validation

• git diff --check passed with no output.
• Runic via Julia 1.10 passed with no output over touched Julia files.
• Direct rendered docs QA for Optimization: Public API documentation | 2 pass / 2 total.
• Direct rendered docs QA for OptimizationBase: Public API documentation | 2 pass / 2 total.
• GROUP=QA Pkg.test on Julia 1.10: QA | 17 pass, 1 broken, 18 total; Testing Optimization tests passed.
• GROUP=OptimizationBase_QA Pkg.test on Julia 1.10: QA | 17 pass, 1 broken, 18 total; Testing OptimizationBase tests passed; Testing Optimization tests passed.
• GROUP=OptimizationOptimJL_QA Pkg.test on Julia 1.10: Quality Assurance | 17 pass, 1 broken, 18 total; Testing OptimizationOptimJL tests passed; Testing Optimization tests passed.
• GROUP=OptimizationPRIMA_QA Pkg.test on Julia 1.10: Quality Assurance | 17 pass, 1 broken, 18 total; Testing OptimizationPRIMA tests passed; Testing Optimization tests passed.
• docs/make.jl on Julia 1.10 passed after local docs env resolution; final output reached HTMLWriter: rendering HTML pages and skipped deployment outside CI. Linkcheck emitted existing redirect warnings.

[ChrisRackauckas-Claude]

Follow-up pushed: bc9120ae7.

This addresses the two rendered-docs QA failures seen on CI:

• OptimizationMadNLP: solve! is an ambiguous backend/OptimizationBase reexport already ignored for docstring ownership, so it is now also ignored for rendered coverage.
• OptimizationMetaheuristics: summary is an ambiguous backend/Base reexport already ignored for docstring ownership, so it is now also ignored for rendered coverage.

Local validation:

• git diff --check: passed.
• Runic on the two touched QA files: passed.
• lib/OptimizationMetaheuristics routed QA passed: Quality Assurance | 16 pass, 2 broken, 18 total.
• lib/OptimizationMadNLP/test/qa/qa.jl direct QA passed: Quality Assurance | 16 pass, 2 broken, 18 total.

The OptimizationBBO Core CI failure is separate from this rendered-docs change: core_tests.jl:188-189 got different stochastic multi-objective values for Rosenbrock/Ackley. I did not loosen or skip that behavioral test in this docs/QA PR.