Cannot find module 'class-transformer' or its corresponding type declarations

I am trying to use the class-transformer package with NestJS v7. The class-transformer package was installed with npm i class-transformer --save. I've followed instructions as per readme.md

This package does have a typescript definition, I can see it on my filesystem (in the correct directory inside node_modules), VS Code navigates to the definition just fine, so I am completely baffled why it isn't working. I've tried removing my node_modules directory, clearing my NPM cache and reinstalling everything again with npm install.

When I try to compile, I just get Cannot find module 'class-transformer' or its corresponding type declarations.

My entity code:

import {
    Column,
    Entity,
    Index,
    OneToMany,
    PrimaryGeneratedColumn,
} from "typeorm";
import { Expose } from 'class-transformer';

@Entity("country", { schema: "my_schema" })
export class Country {
    @PrimaryGeneratedColumn({ type: "int", name: "id" })
    id: number;

    // Some properties here

    @Expose()
    get name(): string {
        return this.someProperty.content;
    }
    ...
}

My tsconfig.json:

{
  "compilerOptions": {
    "target": "es2017",
    "module": "commonjs",
    "moduleResolution": "node",
    "emitDecoratorMetadata": true,
    "experimentalDecorators": true,
    "sourceMap": false,
    "outDir": "./dist",
  }
}

My package.js:

{
  "name": "project-name",
  "version": "0.0.1",
  "description": "",
  "author": "",
  "private": true,
  "license": "UNLICENSED",
  "scripts": {
    "prebuild": "rimraf dist",
    "build": "nest build",
    "format": "prettier --write \"src/**/*.ts\" \"test/**/*.ts\"",
    "start": "nest start",
    "start:dev": "nest start --watch",
    "start:debug": "nest start --debug 0.0.0.0:9229 --watch",
    "start:prod": "node dist/main",
    "lint": "eslint \"{src,apps,libs,test}/**/*.ts\" --fix",
    "test": "jest",
    "test:watch": "jest --watch",
    "test:cov": "jest --coverage",
    "test:debug": "node --inspect-brk -r tsconfig-paths/register -r ts-node/register node_modules/.bin/jest --runInBand",
    "test:e2e": "jest --config ./test/jest-e2e.json"
  },
  "dependencies": {
    "@nestjs/common": "^7.4.2",
    "@nestjs/config": "^0.5.0",
    "@nestjs/core": "^7.0.0",
    "@nestjs/platform-express": "^7.0.0",
    "@nestjs/typeorm": "^7.1.0",
    "class-transformer": "^0.3.1",
    "mysql": "^2.18.1",
    "rimraf": "^3.0.2",
    "rxjs": "^6.5.4",
    "typeorm": "^0.2.25"
  },
  "devDependencies": {
    "@nestjs/cli": "^7.0.0",
    "@nestjs/schematics": "^7.0.0",
    "@nestjs/testing": "^7.0.0",
    "@types/express": "^4.17.3",
    "@types/jest": "25.2.3",
    "@types/node": "^13.9.1",
    "@types/supertest": "^2.0.8",
    "@typescript-eslint/eslint-plugin": "3.0.2",
    "@typescript-eslint/parser": "3.0.2",
    "eslint": "7.2.0",
    "eslint-config-prettier": "^6.10.0",
    "eslint-plugin-import": "^2.20.1",
    "jest": "26.0.1",
    "prettier": "^1.19.1",
    "supertest": "^4.0.2",
    "ts-jest": "26.1.0",
    "ts-loader": "^6.2.1",
    "ts-node": "^8.6.2",
    "tsconfig-paths": "^3.9.0",
    "typescript": "^3.7.4"
  },
  "jest": {
    "moduleFileExtensions": [
      "js",
      "json",
      "ts"
    ],
    "rootDir": "src",
    "testRegex": ".spec.ts$",
    "transform": {
      "^.+\\.(t|j)s$": "ts-jest"
    },
    "coverageDirectory": "../coverage",
    "testEnvironment": "node"
  }
}

I've spent 2 frustrating hours trying to work out why this is the case. This is the only package I've had this kind of issues with, and looking at my config, the package itself and everything else, it makes no sense whatsoever to me.