Database connectivity errors are not propagated

### Step 2: Describe your environment

* Operating System version: all
* Firebase SDK version: 10+
* Firebase Product: database
* Node.js version: all
* NPM version: all

### Step 3: Describe the problem

Errors in connecting to the database are not propagated to user's code. Instead, the library will wait indefinitely when an attempt is made to read or write to the database.

#### Steps to reproduce:

Provide either:
* valid credentials that do not have correct scopes or permissions to access the database
* invalid database url

App initialization will succeed.

Attempt to read or write to the database, triggering an attempt to connect to the database.

Errors will be written to the console, but the error handlers (either the callback on set() or promise rejections) will not be called.

Example error in logs:
```
@firebase/database: FIREBASE WARNING: Firebase error. Please ensure that you have the URL of your Firebase Realtime Database instance configured correctly.
```

Note that this is appears to be a change going from v9 to v10 of the firebase-admin library.

#### Relevant Code:

```
const firebase = require('firebase-admin');

const app = firebase.initializeApp({
credential: credentialWithoutPermissions, // only one of these mistakes is required.
databaseURL: wrongDatabaseUrl,
});

const db = firebase.database();

db.ref('foo').get().then(
() => {
// won't be called because it won't succeed
},
err => {
// won't be called because the failure doesn't propagate
});
```

Start by reproducing the failure with the provided firebase-admin initialization and database read example, using an invalid database URL or insufficient permissions. Compare the behavior between SDK versions 9 and 10, then trace database connection failures through the read/write error handling. Done means callbacks receive the error and promise-based operations reject instead of waiting indefinitely.

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