How to automatically update a Flutter Mobile app to newer version when the application is not on play store or app store?

let's say i have a Flutter APK hosted on my website where users can download and install , what i'm interested to know is how possible that the application can check for newer version when the app lunches and if true a progress bar appears showing the automatic updating of the application from the server (not play store or app store) ? .
here is a company that do exactly the mentioned above meaning :

• download the apk from there server
• whenever a new version is released the app will update from their server

any ideas how to achieve this ?

i found this package ota_update 2.4.1,looks very promising for updating a Flutter from a remote hosted Apk here is an exmple :

   // IMPORT PACKAGE
    import 'package:ota_update/ota_update.dart';
    
      // RUN OTA UPDATE 
      // START LISTENING FOR DOWNLOAD PROGRESS REPORTING EVENTS
      try {
          //LINK CONTAINS APK OF FLUTTER HELLO WORLD FROM FLUTTER SDK EXAMPLES
          OtaUpdate()
              .execute(
            'https://internal1.4q.sk/flutter_hello_world.apk',
            // OPTIONAL
            destinationFilename: 'flutter_hello_world.apk',
            //OPTIONAL, ANDROID ONLY - ABILITY TO VALIDATE CHECKSUM OF FILE:
            sha256checksum: "d6da28451a1e15cf7a75f2c3f151befad3b80ad0bb232ab15c20897e54f21478",
          ).listen(
            (OtaEvent event) {
              setState(() => currentEvent = event);
            },
          );
      } catch (e) {
          print('Failed to make OTA update. Details: $e');
      }

any other proposed solutions are welcome.