Migrate backend from JavaScript to TypeScript and TDD.

[hiyaryan]

This PR is for the backend migration from JavaScript to TypeScript.

Initial commit

• Adds the tsconfig.json file.
• Moves and renames index.js to src/index.ts.
• Updates package.json dev script to use tsx with hot reload. Adds build, start, and start:prod scripts to package.json.
• Adds pm2, tsx, and typescript to dev dependencies.

With these changes, the backend can now transpile TypeScript code to JavaScript.

TypeScript migration strategy

With strict mode on, types may not be inferred. Therefore, it is best to work incrementally.

The following is a strategy that can be used for the migration.

1. Rename a file from .js to .ts
2. Write unit tests for file.
3. Make unit tests pass by resolving any errors, TS or newly discovered.
4. Perform manual end-to-end testing.
5. Commit and repeat.

This PR closes #139

[hiyaryan]

Stricter settings have been turned on in tsconfig. This includes,

• noImplicitAny
• noImplicitThis
• noEmitOnError
• strictNullChecks

See Moving to TypeScript Files for rationale.

[hiyaryan]

Note on CodeFactor issues. We can resolve any remaining at the end of this PR when we're ready to merge into main, or in our sub-PRs if we come across them.