Stack with circular progress bar and elevated button in flutter

You can use package to make your UI more responsive, instead of MediaQuery.

I have done your screen using package. Please try this out. I assumed the heights, widths, and radius. You can modify these as per your requirement. I have also attached the UI I got.

import 'package:flutter/material.dart';
import 'package:flutter_screenutil/flutter_screenutil.dart';

void main() {
  runApp(const MyApp());
}

class MyApp extends StatelessWidget {
  const MyApp({Key? key}) : super(key: key);
  @override
  Widget build(BuildContext context) {
    return ScreenUtilInit(
        designSize: const Size(375, 667),
        minTextAdapt: true,
        builder: () {
          return MaterialApp(
            title: 'Flutter Demo',
            theme: ThemeData(
              primarySwatch: Colors.blue,
            ),
            home: const ButtonTest(),
          );
        });
  }
}

class ButtonTest extends StatefulWidget {
  const ButtonTest({Key? key}) : super(key: key);

  @override
  _ButtonTestState createState() => _ButtonTestState();
}

class _ButtonTestState extends State {
  @override
  Widget build(BuildContext context) {
    return Scaffold(
      backgroundColor: Colors.black,
      body: Center(
        child: Container(
          height: 94.h, // You can change here
          decoration: BoxDecoration(
            shape: BoxShape.circle,
            border: Border.all(
              color: Colors.white,
            ),
          ),
          child: Padding(
            padding: EdgeInsets.all(
              2.0.w, // You can change here
            ),
            child: GestureDetector(
              onTap: () {
                print("Button Pressed");
              },
              child: Container(
                height: 92.h, // You can change here
                width: 92.h, // You can change here
                decoration: const BoxDecoration(
                  shape: BoxShape.circle,
                  gradient: LinearGradient(
                    colors: [
                      Colors.red,
                      Colors.orange,
                    ],
                  ),
                ),
                child: const Center(
                    child: Text(
                  'child',
                  style: TextStyle(
                    color: Colors.white,
                    fontWeight: FontWeight.bold,
                  ),
                )),
              ),
            ),
          ),
        ),
      ),
    );
  }
}

Re wrote your code and here is my output

Transform.scale(
    scale: mediaq.width> 375 ? 3.10 : 2.35,
    child: const CircularProgressIndicator(
      backgroundColor: Colors.white,
      color: Colors.white,
      strokeWidth: .75,
      value: 1,
    ),
  ),

Output: Iphone 12 Pro Max (W:428 , H:926)

Iphone SE (Second Generation) (W:375, H: 667)

Also you can try this package for responsive ui.