Refactoring Provider setup of Google Auth

src/lib/components/GoogleAuth.svelte

@@ -1,23 +1,15 @@
 <script lang="ts">
 	import { onMount, tick } from 'svelte';
-	import {
-		LitAuthClient,
-		BaseProvider,
-		GoogleProvider,
-		isSignInRedirect,
-		getProviderFromUrl
-	} from '@lit-protocol/lit-auth-client';
-	import { LitNodeClient } from '@lit-protocol/lit-node-client';
+	import { isSignInRedirect, getProviderFromUrl } from '@lit-protocol/lit-auth-client';
 	import { IRelayPKP } from '@lit-protocol/types';
 	import { ProviderType } from '@lit-protocol/constants';
 	import { LitAccessControlConditionResource, LitAbility } from '@lit-protocol/auth-helpers';
 	import { createMessage } from '$lib/services/messages';
+	import { setupLitProvider } from '$lib/services/litProviderSetup.ts';
 
 	const redirectUri = 'http://localhost:5173/';
 	let view = 'sign_in';
 	let error;
-	let litAuthClient;
-	let litNodeClient;
 	let currentProviderType;
 	let authMethod;
 	let pkps = [];
@@ -25,7 +17,7 @@
 	let sessionSigs;
 	let isLoading = false;
 
-	let provider: BaseProvider | undefined;
+	let provider;
 
 	onMount(async () => {
 		isLoading = true;
@@ -37,21 +29,8 @@
 		});
 
 		try {
-			litNodeClient = new LitNodeClient({
-				litNetwork: 'serrano',
-				debug: false
-			});
-			await litNodeClient.connect();
-
-			litAuthClient = new LitAuthClient({
-				litRelayConfig: {
-					relayApiKey: 'test-api-key'
-				},
-				litNodeClient
-			});
-
 			// Globally set the provider during the component's mount
-			provider = litAuthClient.initProvider<GoogleProvider>(ProviderType.Google);
+			provider = await setupLitProvider();
 
 			console.log('Checking if isSignInRedirect...');
 			if (!authMethod && isSignInRedirect(redirectUri)) {
@@ -204,7 +183,6 @@
 			view = 'CREATING_SESSION';
 
 			const litResource = new LitAccessControlConditionResource('*');
-			const provider = litAuthClient.getProvider(currentProviderType);
 			sessionSigs = await provider.getSessionSigs({
 				pkpPublicKey: pkp.publicKey,
 				authMethod,