feat(js_interop_gen): support TS Compiler API and resolve all type-system errors

Migrate js_interop_gen parser infrastructure to use the TypeScript Compiler API bindings.

- Add generated TypeScript API bindings in lib/src/js/generated/typescript_api.dart and binding update script.
- Refactor AST nodes, type representation, and parser logic to interface with the TypeScript Compiler API.
- Fix sub-type hierarchy, type mapping, and union casting resolution.
- Restore SDK-internal formatting for golden test expected files and update generator goldens.