feat(firebaseai): server prompt chat and function calling (#17972)

* add chat and function back to server prompt template

* auto function calling for server prompt template

* update with api decision

* add tool structure

* kts support

* fix compile error for server template page

* Add auto function calling to chat stream, and add test cases

* add tools and toolConfig into template request

* fix the template function name and update the schema override sample

* add too config

* some fix for e2e test

* fix analyzer

* tiny year change

* bot review comment

* fix analyzer and formatter

* remove unrelated files from  PR

* fix formatter

Author: cynthiajoan

packages/firebase_ai/firebase_ai/example/lib/pages/function_calling_page.dart

@@ -15,6 +15,7 @@
 import 'package:flutter/material.dart';
 import 'package:firebase_ai/firebase_ai.dart';
 import 'package:firebase_auth/firebase_auth.dart';
+import '../utils/function_call_utils.dart';
 import '../widgets/message_widget.dart';
 
 class FunctionCallingPage extends StatefulWidget {
@@ -31,13 +32,6 @@ class FunctionCallingPage extends StatefulWidget {
   State<FunctionCallingPage> createState() => _FunctionCallingPageState();
 }
 
-class Location {
-  final String city;
-  final String state;
-
-  Location(this.city, this.state);
-}
-
 class _FunctionCallingPageState extends State<FunctionCallingPage> {
   late GenerativeModel _functionCallModel;
   late GenerativeModel _autoFunctionCallModel;
@@ -80,7 +74,7 @@ class _FunctionCallingPageState extends State<FunctionCallingPage> {
               'The date for which to get the weather. Date must be in the format: YYYY-MM-DD.',
         ),
       },
-      callable: _fetchWeatherCallable,
+      callable: fetchWeatherCallable,
     );
     _autoFindRestaurantsTool = AutoFunctionDeclaration(
       name: 'findRestaurants',
@@ -231,16 +225,6 @@ class _FunctionCallingPageState extends State<FunctionCallingPage> {
     };
   }
 
-  Future<Map<String, Object?>> _fetchWeatherCallable(
-    Map<String, Object?> args,
-  ) async {
-    final locationData = args['location']! as Map<String, Object?>;
-    final city = locationData['city']! as String;
-    final state = locationData['state']! as String;
-    final date = args['date']! as String;
-    return fetchWeather(Location(city, state), date);
-  }
-
   void _initializeModel() {
     final generationConfig = GenerationConfig(
       thinkingConfig: _enableThinking
@@ -301,23 +285,6 @@ class _FunctionCallingPageState extends State<FunctionCallingPage> {
     );
   }
 
-  // This is a hypothetical API to return a fake weather data collection for
-  // certain location
-  Future<Map<String, Object?>> fetchWeather(
-    Location location,
-    String date,
-  ) async {
-    // TODO(developer): Call a real weather API.
-    // Mock response from the API. In developer live code this would call the
-    // external API and return what that API returns.
-    final apiResponse = {
-      'temperature': 38,
-      'chancePrecipitation': '56%',
-      'cloudConditions': 'partly-cloudy',
-    };
-    return apiResponse;
-  }
-
   /// Actual function to demonstrate the function calling feature.
   final fetchWeatherTool = FunctionDeclaration(
     'fetchWeather',