I have a Node.js server, inside which I want to have two firebase instances.

One instance should use the JavaScript SDK and will be used to provide authentication - login/register. The other instance should use the Admin SDK and will be used to read/write from the Realtime Database. I want to use this approach, so that I don't have to authenticate the user before each request to the Realtime DB.

I've read how we're supposed to initialize Firebase instances for multiple projects, but I'm not sure if my issue isn't coming from the fact that both instances are for the same project.
My issue is that I can use the JS SDK without any issue and I can login/register the user, but for some reason I can't get the Admin SDK to work.
Here's how I'm instantiating the apps:

const admin = require("firebase-admin");
const { applicationDefault } = require('firebase-admin/app');

admin.initializeApp({
  credential: applicationDefault(),
  databaseURL: 'my-database-url'
}, 'adminApp');


const firebase = require("firebase/app");
firebase.initializeApp(my-config);

Now I can use the JS SDK without an issue, but not the Admin SDK. I've created a test endpoint to just get data from my Realtime DB:

app.get("/api/test", (req, res) => {
  const uid = 'my-user-UID';
  admin.database().ref(`users/${uid}`)
    .once('value', (snapshot) => {
      if(snapshot) {
        console.log('data');
      } else {
        console.log('no data');
      }
  });
});

Now here as an approach to getting the data from the Realtime DB, I tried all possible described approaches. Using get with child and all sorts of possible combinations. Here's an example of another approach I used:

  get(child(ref(admin.database()), `users/${uid}`)).then((snapshot) => {
    if (snapshot.exists()) {
      // retrieved data
    } else {
      // No data
    }
  }).catch((error) => {
    console.error(error);
  });

For the first approach I wasn't getting any response at all, like the once wasn't executing. For the second one I think I was getting - typeerror: pathstring.replace is not a function firebase. At some point I was getting a no firebase app '[default]' has been created . These errors don't worry me as much, but since I saw the last error I moved my focus to the initialization of the apps, but still to no avail.
I just need a direction of where my issue might be coming from.

Update:

The solution is to not pass a second argument (app name) to any of the Firebase initializations. Looks like it's not needed in case you're referencing the same project.