You can fix by doing this

class WeatherService {
  //static const BASE_URL = 'https://api.openweathermap.org/data/2.5/forecast?q=Kutahya,tr&cnt=5&appid=e6080829dff63e16ef3e9756b2e4b0bd';
  static const baseUrl = 'https://api.openweathermap.org/data/2.5/weather?';
  final String apiKey;

  WeatherService({required this.apiKey});

  Future<Map<String, dynamic>> getWeather(String city, String country) async {
    final response = await http.get(Uri.parse('$baseUrl?q=$city,$country&appid=$apiKey&units=metric'));

    if (response.statusCode == 200) {
      return jsonDecode(response.body);
    } else {
      throw Exception('Failed to get Data');
    }
  }
}

Your code looks great, but the mistake you made is calling your getWeather function in the constructor. To use this function, you should call it outside of the constructor. That way, you can use the function properly

class DemoClass {
  String yourKey;

  // Constructor
  DemoClass(this.yourKey);


 // Outside of the constructor
  Future<String> yourFunction() async {
    return "Your API response";
  }
}

I would also suggest using proper state management to achieve performance improvements in your application.

Try below code hope its help to you.

WeatherService

class WeatherService {
  static const baseUrl = 'https://api.openweathermap.org/data/2.5/forecast';
  final String apiKey;

  WeatherService(this.apiKey);

  Future<WeatherModel> getWeather(String city, String country) async {
    final response = await http.get(
      Uri.parse('$baseUrl?q=$city,$country&appid=$apiKey&units=metric'),
    );

    if (response.statusCode == 200) {
      return WeatherModel.fromJson(jsonDecode(response.body));
    } else {
      throw Exception('Failed to get Data');
    }
  }
}

WeatherPage

class WeatherPage extends StatefulWidget {
  const WeatherPage({super.key});

  @override
  State<WeatherPage> createState() => _WeatherPageState();
}

class _WeatherPageState extends State<WeatherPage> {
   final WeatherService weatherService = WeatherService('e6080829dff63e16ef3e9756b2e4b0bd');
  WeatherModel? weather;
  WeatherModel? fetchedWeather;
  bool isLoading = false;
  String errorMessage = '';
  //set city and country
  String city = 'Kutahya'; //You may use Geolocator to get them automatically also.
  String country = 'tr';

  @override
  void initState() {
    super.initState();
    fetchWeatherData();
  }

  Future<void> fetchWeatherData() async {
    setState(() {
      isLoading = true;
      errorMessage = '';
    });

    try {
      fetchedWeather = await weatherService.getWeather(city, country);
      setState(() {
        weather = fetchedWeather!;
      });
    } catch (error) {
      setState(() {
        errorMessage = 'Failed to load weather data: $error';
      });
    } finally {
      setState(() {
        isLoading = false;
      });
    }
  }

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(title: Text('Weather')),
      body: isLoading
          ? Center(child: CircularProgressIndicator())
          : errorMessage.isNotEmpty
              ? Center(child: Text(errorMessage))
              : weather != null
                  ? Center(
                      child: ListView.builder(
                        itemCount: weather!.list!.length,
                        itemBuilder: (context, index) {
                          return Text(weather!
                              .list![index].weather![0].description
                              .toString());
                        },
                      ),
                    )
                  : Center(child: Text('No weather data')),
    );
  }
}

I have try some Data on UI:

weather_service.dart

place getWeather method outside the constructor

import 'dart:convert';
import 'package:testapp/models/weather_model.dart';
import 'package:http/http.dart' as http;

class WeatherService {
  //static const BASE_URL = 'https://api.openweathermap.org/data/2.5/forecast?q=Kutahya,tr&cnt=5&appid=e6080829dff63e16ef3e9756b2e4b0bd';
  static const baseUrl = 'https://api.openweathermap.org/data/2.5/weather?';
  final String apiKey; //The “final” keyword is used to declare variables whose values cannot be changed once assigned. When a variable is declared as final, it can only be assigned a value once, either at its declaration or within the constructor of the class.

  WeatherService(this.apiKey);
    Future<Weather> getWeather(String city, String country) async {
      final response = await http.get(Uri.parse('$baseUrl?q=$city,$country&appid=$apiKey&units=metric'));

      if (response.statusCode == 200) {
        return Weather.fromJson(jsonDecode(response.body));
      } else {
        throw Exception('Failed to get Data');
      }
    }
}

call _featchWeather() inside initState()

weather_page.dart


   @override
void initState(){
super.initState();
_fetchWeather();
}

_fetchWeather() async{
try{
final weather = await _weatherService.getWeather(city,country);
setState((){
_weather = weather;
});
}
catch(e){
print(e);
}
}