Need to connect to secondary app instances automatically with the current user in Firebase Web

I’m working with Firebase Web. I'm using multiple databases in the same project for scalability purposes. I’m not sure how to connect to a secondary database (this will be a dynamic DB) with the current authenticated user?

This is my current code:

let secondary_app = firebase.initializeApp(
      { ...config, databaseURL: secondaryDbUrl },
      "secondary_app"
    );
let query = firebase.database(secondary_app).ref(rtdbPath);

But this won't have the current user's authentication and hence all security rules that require auth fail.

The problem is that my secondary Db URLs are dynamic and I have to do reinitialization multiple times in the code. Should I have to sign in into the secondary app instance every time I create a secondary app through firebase.initializeApp?

Non-web SDKs seem to have a much easier approach where you are allowed to enter the Database URL directly into firebase.database() as an argument. Does a similar easier approach exist for Web SDK? Thanks for the help in advance!