TypeScript - Can't find module defined as path alias

I've added a path alias to my TypeScript project to make the importing a bit more manageable, however, I get an error when I run the compiled JavaScript.

When I run: node ./bin/index.js

The response is:

node:internal/modules/cjs/loader:936
  throw err;
  ^

Error: Cannot find module '@castorApp/CastorApp'

This way I import is:

import { CastorApp } from "@castorApp/CastorApp";

my folder structure is:

CastorJS/
├─ node_modules/
├─ bin/
├─ src/
│  ├─ castorApp/
│  │  ├─ CastorApp.ts
│  │  ├─ CommandService.ts
│  ├─ types/
│  ├─ index.ts
├─ .gitignore
├─ package-lock.json
├─ package.json
├─ tsconfig.json

my tsconfig.json looks like this:

{
    "compilerOptions": {
        "module": "commonjs",
        "target": "es2017",
        "lib": [
            "es2015"
        ],
        "moduleResolution": "node",
        "sourceMap": true,
        "outDir": "bin",
        "baseUrl": ".",
        "paths": {
            "*": [
                "node_modules/*",
                "src/types/*"
            ],
            "@castorApp*": [
                "src/castorApp",
                "src/castorApp*"
            ]
        },
        "emitDecoratorMetadata": true,
        "experimentalDecorators": true
    },
    "include": [
        "src/**/*"
    ]
}

My package.json looks like this:

{
  "name": "castor",
  "version": "1.0.0",
  "description": "TypeScript version of Castor",
  "main": "bin/index.js",
  "scripts": {
    "build": "tsc",
    "test": "echo \"Error: no test specified\" && exit 1"
  },
  "author": "ZtModArchive",
  "license": "MIT",
  "dependencies": {
    "@types/node": "^18.7.18"
  },
  "devDependencies": {
    "typescript": "^4.8.3"
  }
}

I've seen someone on a blog post recommend the module-alias package, however the package has the following warning on its readme:

WARNING: This module should not be used in other npm modules since it modifies the default require behavior! It is designed to be used for development of final projects i.e. web-sites, applications etc.

And so, since I do wish to publish my code as a package, this is unfortunately not an option.