Update auth compat to be properly typed in typescript (#4626)

* Add proper typings for auth compat package

* Formatting

* Fix linter

* Formatting

Author: sam-gc

packages-exp/app-compat/src/index.ts

@@ -47,4 +47,4 @@ registerCoreComponents();
 export default firebase;
 
 export { _FirebaseNamespace, _FirebaseService } from './types';
-export { FirebaseApp } from './public-types';
+export { FirebaseApp, FirebaseNamespace } from './public-types';

packages-exp/auth-compat-exp/index.ts

@@ -24,6 +24,7 @@ import {
   InstantiationMode
 } from '@firebase/component';
 
+import { FirebaseAuth } from '@firebase/auth-types';
 import { version } from './package.json';
 import { Auth } from './src/auth';
 import { Persistence } from './src/persistence';
@@ -33,6 +34,23 @@ import { RecaptchaVerifier } from './src/recaptcha_verifier';
 
 const AUTH_TYPE = 'auth';
 
+declare module '@firebase/component' {
+  interface NameServiceMapping {
+    'auth-compat': FirebaseAuth;
+  }
+}
+
+declare module '@firebase/app-compat' {
+  interface FirebaseNamespace {
+    auth: {
+      (app?: FirebaseApp): FirebaseAuth;
+    };
+  }
+  interface FirebaseApp {
+    auth?(): FirebaseAuth;
+  }
+}
+
 // Create auth components to register with firebase.
 // Provides Auth public APIs.
 function registerAuthCompat(instance: _FirebaseNamespace): void {