AppHosting Firebase: Need to provide options, when not being deployed to hosting via source. (app/no-options)

### Operating System

macOS 14.5

### Environment (if applicable)

NextJS 15

### Firebase SDK Version

12.2.1

### Firebase SDK Product(s)

Auth

### Project Tooling

I'm using NextJS with Firebase on app hosting. I'm testing with `firebase emulators:start --only apphosting`

### Detailed Problem Description

I'm trying to use the no-config initialization of Firebase as describe here: https://firebase.google.com/docs/app-hosting/firebase-sdks#initialize-with-no-arguments.
However it always fails during apphosting emulator testing with the error `Firebase: Need to provide options, when not being deployed to hosting via source. (app/no-options)`.

I even tried to specify the configuration during Firebase install (`FIREBASE_WEBAPP_CONFIG="{...}" npm install firebase`) however this also doesn't work. I checked the generated files where the config should be stored and they just look like this:
```javascript
'use strict';
Object.defineProperty(exports, '__esModule', { value: true });
exports.getDefaultsFromPostinstall = () => (undefined);
```

I guess, instead of `undefined` there should be my configuration.

Why can't NPM get the config during post install?
And how should this normally work because if I understand the manual correctly, it should even work without specifying any config env var during install or does this simply not work with NextJS?

### Steps and code to reproduce issue

```javascript
"use client";

import { initializeApp } from "firebase/app";
import { getAuth } from "firebase/auth";
import { getFirestore } from "firebase/firestore";
import { getRemoteConfig } from "firebase/remote-config";
import { getStorage } from "firebase/storage";

const firebaseApp = initializeApp();

export const auth = getAuth(firebaseApp);
export const firestore = getFirestore(firebaseApp);
export const remoteConfig = getRemoteConfig(firebaseApp);
export const storage = getStorage(firebaseApp);
```