If you want to use compat version of Firebase SDK then you would have to import compat version of other Firebase services too. Try refactoring the code as shown below:

import firebase from "firebase/compat/app";
import 'firebase/compat/storage';
import 'firebase/compat/firestore';

const firebaseConfig = {...};

// Initialize Firebase
const app = firebase.initializeApp(firebaseConfig);
// with firebase. namespace

const projectStorage = firebase.storage();
const projectFirestore = firebase.firestore();

export {
    projectStorage,
    projectFirestore
};

However, I would recommend using the Modular SDK and initialize Firebase like this:

import { initializeApp } from "firebase/app";
import { getStorage } from 'firebase/storage';
import { getFirestore } from 'firebase/firestore';

const firebaseConfig = {...};

// Initialize Firebase
const app = initializeApp(firebaseConfig);

const projectStorage = getStorage();
const projectFirestore = getFirestore();

export {
    projectStorage,
    projectFirestore
};

Also checkout Getting started with Firebase for the web