docs: specify DataDrivenDiffEq developer interfaces

[ChrisRackauckas-Claude]

Summary

This is a focused follow-up to the compat-only #650 and does not modify or supersede it.

• Audit the root and DataDrivenDMD, DataDrivenLux, DataDrivenSR, and DataDrivenSparse sublibraries for SciMLStyle documentation.
• Put detailed docstrings on the original definitions, including arguments, keywords, returns, examples, fields, and extension contracts.
• Add rendered documentation entries for every newly public developer interface.
• Add generic interface tests for the DMD Koopman, Lux DAG symbolic-regression, and sparse-regression extension points.
• Keep the reexported solve ownership explicit: its generic docstring belongs to CommonSolve, while this package documents DataDrivenDiffEq usage.
• Keep SciMLTesting's existing 2.4 lower bound in QA environments; no repository-specific rendered/doctest overrides are used.

The abstract extension interfaces are versioned developer API for solver packages. Ordinary users should use the concrete problem, basis, solver, and solution APIs.

Verification

• Root GROUP=QA julia --project=. --startup-file=no -e 'using Pkg; Pkg.test()': passed, Quality Assurance | 20 20 and JET Static Analysis | 11 11.
• DataDrivenDMD GROUP=QA: passed, QA | 21 21.
• DataDrivenLux GROUP=QA: passed, QA | 21 21.
• DataDrivenSR GROUP=QA: passed, Quality Assurance | 21 21.
• DataDrivenSparse GROUP=QA: passed, QA | 21 21.
• Generic interface tests: DMD 8/8, Lux 2/2, Sparse 9/9.
• julia --project=docs --startup-file=no -e 'using Pkg; Pkg.develop(PackageSpec(path=pwd())); include("docs/make.jl")': completed successfully. Only existing redirect and large-example rendering warnings were emitted.
• Julia Runic check, typos, and git diff --check: passed.

The open #650 DMD Core failures are pre-existing. On the clean base branch, the same test errors at lib/DataDrivenDMD/test/Core/nonlinear_autonomous.jl with UndefVarError: DiscreteProblem not defined; this follow-up does not change that test.

Please ignore this draft until reviewed by @ChrisRackauckas.