Browserify - ParseError: 'import' and 'export' may appear only with 'sourceType: module'

I would like to make code transpiled by TypeScript to JavaScript be able to run in the browser:

ka@Karl-Laptop MINGW64 ~/Development/async (km/client-library)
$ npx browserify ./dist/index.js -t babelify -o ./dist/bundle.js

C:\Users\karl\Development\async\dist\index.js:1
export * from './shared';
^
ParseError: 'import' and 'export' may appear only with 'sourceType: module'

I read the following: https://babeljs.io/setup#installation via clicking on the browserify button. But it didn't help at all (I installed npm install --save-dev babelify babel-core --save-exact and ran npx browserify ./dist/index.js -t babelify -o ./dist/bundle.js, same error).

./dist/index.js file:

export * from './shared';
export * from './client';
export * from './server';
//# sourceMappingURL=index.js.map

tsconfig.js file:

{
    "compilerOptions": {
        "target": "ES5",
        "module": "ES2015",
        "declaration": true,
        "lib": ["ES2016", "ES2017", "ES2018", "ES2019", "ES2018", "ES2019", "ES2020", "dom"],
        "moduleResolution": "node",
        "sourceMap": true,
        "outDir": "./dist/",
        "removeComments": true,
        "esModuleInterop": true,
        "baseUrl": ".",
        "resolveJsonModule": true,
        "strict": true,
        "noEmitOnError": true,
        "noFallthroughCasesInSwitch": true,
        "noImplicitReturns": true,
        "types": ["node", "jest"]
    },
    "exclude": ["./dist/", "./coverage/", "./report/"],
    "include": ["./src/**/*"]
}

So from TypeScript -> Javascript -> ES5. As per usual I'm guessing Babel is needed to be configured but I am lost as to what exactly it needs.