Convert Entire JavaScript Codebase to TypeScript

Use this plan when a JS codebase needs stronger correctness guarantees and IDE support via TypeScript.

## Steps:

1. Add TypeScript tooling and create a strict tsconfig.json.

2. Enable allowJs and incremental migration in the config.

3. Rename entry points and shared modules to .ts/.tsx one slice at a time.

4. Fix the most critical implicit any/type errors in shared utilities.

5. Introduce interfaces and types for core domain models.

6. Gradually tighten compiler options (noImplicitAny, strictNullChecks).

7. Add type-checking to CI as a required step.

8. Remove allowJs once all critical files are migrated.