Omitting app name in initialization can cause: "FIREBASE FATAL ERROR: Database initialized multiple times" later on

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### [REQUIRED] Step 2: Describe your environment

* Operating System version: macOS Ventura 13.1
* Firebase SDK version: 11.19.0
* Firebase Product: database
* Node.js version: v18.12.1
* NPM version: 8.19.2

### [REQUIRED] Step 3: Describe the problem
When initializing an app using initializeApp(), passing options for the app is optional, as is giving the app a name.
Inside of an onCreate event (and maybe other database events too);
and when the `databaseURL` option was used in the initialization, but no app name was given;
and using both the root ref from `getDatabase(getApp([name])).ref()` as wel as using the `snapshot.ref` from the onCreate event
a fatal error: `FIREBASE FATAL ERROR: Database initialized multiple times` occurs. This doesn't error when giving an app name. Explanation is not very clear, but the steps to reproduce are easier to understand the problem.

I can certainly understand that giving a name to the app is favorable, even when only using a single app. But the fact that the behavior is different depending on whether an app name is used or not, makes me think this is a bug rather than a 'feature', especially when using a name for an app is explicitly made optional.

#### Steps to reproduce:

Using the index.ts from next section and triggering the Test onCreate-function, it will crash when everything between `<>` is omitted, but won't crash with an app name given.
Note the use of a reference from both the database as from the snapshot given by onCreate.
It errors (when not using an app name) with the error: `FIREBASE FATAL ERROR: Database initialized multiple times. Please make sure the format of the database URL matches with each database() call.`
It always errors on the second reference use. So in this case it errors on the `snap.ref.…`, but when changing the order between the two lines using `set()`, it will error on `getDatabase(getApp()).ref()`.
Also when `initializeApp` is used without any options, it does not error.
The url given to the `databaseURL` option could be the one from the default realtime database or a secondary one. Of course, when using a secondary one, the `Test` function should also use `instance()` to listen on that same secondary database.

The behavior is the same in the emulator and in production.

#### Relevant Code:

```
import { getApp, initializeApp } from "firebase-admin/app";
import { getDatabase } from "firebase-admin/database";
import * as functions from "firebase-functions";

initializeApp(
{
databaseURL:
"urlToDefaultRDB", // url to either the primary or a secondary realtime database
}
<, "myAppName" >
);

export const Test = functions.database
// .instance("secondary")
.ref("test/{pushID}/")
.onCreate(async (snap) => {
getDatabase(getApp(< "myAppName" >)).ref().child("foobar").set(true); // succeeds
snap.ref.set(!snap.val()); // fatal error when no app name is used
});
```