Document public API and migrate QA to SciMLTesting 2.4

[ChrisRackauckas-Claude]

Summary

• Remove the blanket Catalyst reexport and depend on each owning public API directly.
• Add SciMLStyle definition-site docs and rendered API coverage for all exported names, including the deprecated NaiveIndexHandler forwarding constructor.
• Upgrade to strict SciMLTesting 2.4 defaults with no package-specific QA exclusions, and update examples/tests for explicit Catalyst imports.
• Bump to 0.4.0 because removing the dependency reexport is a public API reduction.

Local checks

• Pkg.test(): 47/47 tests passed.
• Strict SciMLTesting 2.4 QA: 18/18 passed.
• Documenter doctests/checks/HTML rendering passed.
• Runic check passed for all 14 tracked Julia files.

Ignore until reviewed by @ChrisRackauckas.