Nothing I do here seems to work, I can't find an example anywhere that actually seems correct

This:

import { initializeApp } from 'firebase-admin/app';

Throws:

Error [ERR_MODULE_NOT_FOUND]: Cannot find module '\path\to\my-proj\functions\node_modules\firebase-admin\app' imported from \path\to\my-proj\functions\index.js

This:

import * as admin from "firebase-admin";
admin.initializeApp();

Throws:

TypeError: admin.initializeApp is not a function

my functions' package.json looks like:

  "dependencies": {
    "firebase-admin": "^9.12.0",
    "firebase-functions": "^3.20.1"
  },

What's going on, what's the correct syntax?