How can I fetch URLs from an API and loop them into a carousel?

I have tried for the past days to retrieve datas from this API (https://www.bkgchallenge.it/badmin/APIM/getsponsor.php) and loop it into a carousel (I would need to show only the name and get the URL for the image).

import 'package:equatable/equatable.dart';
import 'package:http/http.dart' as http;
import 'package:test_v02/models/models.dart';

class RemoteService {
  Future<List<Sponsor>?> getSponsor() async {
    var client = http.Client();

    var uri =
        Uri.parse('https://www.bkgchallenge.it/badmin/APIM/getsponsor.php');
    var response = await client.get(uri);
    if (response.statusCode == 200) {
      var json = response.body;
      return sponsorFromJson(json);
    }
  }
}

class Category extends Equatable {
  final String imageUrl;
  final String name;

  const Category({
    required this.imageUrl,
    required this.name
  });

  @override
  List<Object?> get props => [imageUrl];

  static List<Category> categories = [
    const Category(
      imageUrl:
          'https://upload.wikimedia.org/wikipedia/commons/9/9a/Gull_portrait_ca_usa.jpg',
      name: 'Seagull',
    ),
    const Category(
      imageUrl:
          'https://upload.wikimedia.org/wikipedia/commons/9/9a/Gull_portrait_ca_usa.jpg',
          name: 'Seagull',
    )
  ];
}

This is the solution I tried to come up with, this page sends the link and the name to the page with the carousel, I don't know however how to extract the URL and the name and insert them into

    const Category(
          imageUrl:
              'https://upload.wikimedia.org/wikipedia/commons/9/9a/Gull_portrait_ca_usa.jpg',
 name: 'Seagull',
        )