How to interact flutter apk with PostgreSQL and external website?

This is the complete code,

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

  @override
  State<Authorize> createState() => _AuthorizeState();
}

class _AuthorizeState extends State<Authorize> {
  late Future<List<dynamic>> _custList;

  @override
  void initState() {
    super.initState();
    //_futureList = fetchListData();
    _custList = ModelsPositions().getCust();
  }

  _launchURL(String url) async {
    final uri = Uri.parse(url);
    if (await canLaunchUrl(uri)) {
      await launchUrl(uri, mode: LaunchMode.externalApplication);
    } else {
      throw 'Could not launch $url';
    }
  }

  @override
  Widget build(BuildContext context) {
    return Scaffold(
        appBar: AppBar(
          title: const Text('sample orders'),
        ),
        //automaticallyImplyLeading: false),
        body: FutureBuilder<List<dynamic>>(
          future: _custList,
          builder: (context, snapshot) {
            if (snapshot.hasData) {
              List<dynamic> custAPIs = snapshot.data ?? [];
              return ListView.builder(
                  itemCount: custAPIs.length,
                  itemBuilder: (context, index) {
                    String custID = custAPIs[index][0];
                    return Card(
                      child: Row(
                        children: [
                          SizedBox(width: 50),
                          Expanded(
                            child: Text('custID: $custID'),
                          ),
                          SizedBox(width: 15),
                          Expanded(
                            child: ElevatedButton(
                                child: const Text('check'),
                                onPressed: () {
                                  String url =
                                      "https://www.amazon.in/";
                                  _launchURL(url);
                                }),
                          ),
                        ],
                      ),
                    );
                  });
            } else if (snapshot.hasError) {
              return const Center(
                  child: Text('Failed to fetch Positions Summary'));
            }
            return const Center(child: CircularProgressIndicator());
          },
        ));
  }
}

I'm installed apk file in mobile and trying to open from mobile.(When I tried in emulator working fine but after generating apk and installing in mobile it is not opening the webpage).