結論

FlutterのGestureDetectorは１回のタップで１つのイベントしか発火されないようになっているため、RawGestureDetectorを使う必要があります。

import 'package:flutter/gestures.dart';
import 'package:flutter/material.dart';
import 'package:flutter_hooks/flutter_hooks.dart';

class TitleScreen extends HookWidget {
  const TitleScreen({Key? key}) : super(key: key);

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      body: _GetAllScreenTapEventWidget(
        child: Center(
          child: SizedBox(
            width: 100,
            height: 100,
            child: GestureDetector(
              onTap: () => print("button tap event"),
              child: const Card(
                color: Colors.red,
                child: Text('Tap me'),
              ),
            ),
          ),
        ),
      ),
    );
  }
}

class _GetAllScreenTapEventWidget extends HookWidget {
  final Widget child;
  const _GetAllScreenTapEventWidget({
    required this.child,
  });

  @override
  Widget build(BuildContext context) {
    void onTapDown(details) {
      print("all screen tap event");
    }

    return Stack(
      fit: StackFit.expand,
      children: [
        child,
        RawGestureDetector(
          behavior: HitTestBehavior.translucent,
          gestures: <Type, GestureRecognizerFactory>{
            _TapAnimationGestureRecognizer:
                GestureRecognizerFactoryWithHandlers<
                    _TapAnimationGestureRecognizer>(
              () {
                return _TapAnimationGestureRecognizer(onTapDown: onTapDown);
              },
              (_) {},
            ),
          },
        ),
      ],
    );
  }
}

class _TapAnimationGestureRecognizer extends OneSequenceGestureRecognizer {
  _TapAnimationGestureRecognizer({required this.onTapDown});
  final Function(PointerEvent) onTapDown;

  bool _isDown = false;

  @override
  void addAllowedPointer(PointerDownEvent event) {
    startTrackingPointer(event.pointer);
    // イベントを他のオブジェクトに伝搬させるためにrejectする
    resolve(GestureDisposition.rejected);
  }

  @override
  String get debugDescription => 'recognizer for duplicate tap down event';

  @override
  void didStopTrackingLastPointer(int pointer) {}

  @override
  void handleEvent(PointerEvent event) {
    if (event.down) {
      if (!_isDown) {
        onTapDown(event);
        _isDown = true;
      }
    } else {
      _isDown = false;
    }
  }
}