fix(vertexai): hotfix for vertexai auth access to storage (#13534)

* hotfix for vertexai auth access to storage

* remove unused change

Author: cynthiajoan

packages/firebase_vertexai/firebase_vertexai/example/lib/main.dart

@@ -13,6 +13,7 @@
 // limitations under the License.
 
 import 'package:firebase_core/firebase_core.dart';
+import 'package:firebase_auth/firebase_auth.dart';
 import 'package:firebase_vertexai/firebase_vertexai.dart';
 import 'package:flutter/material.dart';
 import 'package:flutter/services.dart';
@@ -90,10 +91,12 @@ class _ChatWidgetState extends State<ChatWidget> {
     super.initState();
 
     initFirebase().then((value) {
-      _model = FirebaseVertexAI.instance.generativeModel(
+      var vertex_instance =
+          FirebaseVertexAI.instanceFor(auth: FirebaseAuth.instance);
+      _model = vertex_instance.generativeModel(
         model: 'gemini-1.5-flash',
       );
-      _functionCallModel = FirebaseVertexAI.instance.generativeModel(
+      _functionCallModel = vertex_instance.generativeModel(
         model: 'gemini-1.5-flash',
         tools: [
           Tool.functionDeclarations([fetchWeatherTool]),
@@ -156,6 +159,7 @@ class _ChatWidgetState extends State<ChatWidget> {
   Future<void> initFirebase() async {
     // ignore: avoid_redundant_argument_values
     await Firebase.initializeApp(options: options);
+    await FirebaseAuth.instance.signInAnonymously();
   }
 
   void _scrollDown() {

packages/firebase_vertexai/firebase_vertexai/lib/src/model.dart

@@ -159,7 +159,7 @@ final class GenerativeModel {
       if (auth != null) {
         final idToken = await auth.currentUser?.getIdToken();
         if (idToken != null) {
-          headers['Authorization'] = idToken;
+          headers['Authorization'] = 'Firebase $idToken';
         }
       }
       return headers;