chore: add typecheck script and enable strict type checking

[thkruz]

Proposed changes

The project had no type-checking step. ESLint is configured with typescript-eslint's recommended ruleset, which only runs syntactic lint rules; it performs no type-checking and there was no tsc invocation anywhere in the npm scripts. As a result, type errors were never caught by npm run lint, CI, or any other command.

Types of changes

It is an adjustment to the build/development process, not a modification to the production code.

• Bug fix (non-breaking change which fixes an issue).
• New feature (non-breaking change which adds functionality).
• Breaking change (fix or feature that would cause existing functionality to change).

Checklist:

• [ x] I have read the CONTRIBUTING document.
• [ x] My commit messages follows the conventional commit format
• My change requires a change to the documentation, and updated it accordingly.
• I have added tests to cover my changes.
• [x ] All new and existing tests passed.