refactor(codegen): generate schema bindings directly

[PsiACE]

Summary

• Replace custom schema parsing and AST post-processing with direct datamodel-code-generator configuration.
• Regenerate the current v1.19 bindings while preserving public names, lenient deserialization, extensible unions, and singleton discriminator defaults.
• Add make gen-check for read-only generation checks.

Related issues

Relates to #47.

Testing

• make gen-check
• make check
• make test (197 passed, 1 skipped)
• uv run mkdocs build --strict
• Loaded every module under examples/

Docs & screenshots

No docs or example changes. This branch only replaces code generation and keeps the current schema and public API.

Checklist

• Conventional Commit title (e.g. feat:, fix:).
• Tests cover the change or are not required (explain above).
• Docs/examples updated when behaviour is user-facing.
• Schema regenerations (make gen-all) are called out if applicable.