Dart Flutter debug in VSCode only works if breakpoint defined in DevTools Debugger

I have a very confusing behavior when I try to debug a really simple app. I just finished this tutorial, https://codelabs.developers.google.com/codelabs/first-flutter-app-pt2#8, so nothing fancy :)

What happens is, break-points are not triggered when they are defined in VSCode. I did some research, and with this topic - Dart Flutter DevTools "Debugger" Tab not showing up - was able to get the debugger tab in DevTools. Funny part is, when I define a break-point in DevTools, then the debugging itself happens in VSCode (even if no break-point).

Obviously, I'd prefer to be able to set up my break-points in VSCode. Thank you for your help!

Some more details :

[flutter] flutter doctor -v
[✓] Flutter (Channel stable, 2.2.3, on macOS 11.2.3 20D91 darwin-arm, locale fr-FR)
    • Flutter version 2.2.3 at /Users/<usr>/SDK/flutter
    • Framework revision f4abaa0735 (il y a 7 semaines), 2021-07-01 12:46:11 -0700
    • Engine revision 241c87ad80
    • Dart version 2.13.4

[✓] Android toolchain - develop for Android devices (Android SDK version 30.0.3)
    • Android SDK at /Users/<usr>/Library/Android/sdk
    • Platform android-30, build-tools 30.0.3
    • Java binary at: /Applications/Android Studio.app/Contents/jre/jdk/Contents/Home/bin/java
    • Java version OpenJDK Runtime Environment (build 1.8.0_242-release-1644-b3-6915495)
    • All Android licenses accepted.

[✓] Xcode - develop for iOS and macOS
    • Xcode at /Applications/Xcode.app/Contents/Developer
    • Xcode 12.5.1, Build version 12E507
    • CocoaPods version 1.10.2

[✓] Chrome - develop for the web
    • Chrome at /Applications/Google Chrome.app/Contents/MacOS/Google Chrome

[✓] Android Studio (version 4.1)
    • Android Studio at /Applications/Android Studio.app/Contents
    • Flutter plugin can be installed from:
       https://plugins.jetbrains.com/plugin/9212-flutter
    • Dart plugin can be installed from:
       https://plugins.jetbrains.com/plugin/6351-dart
    • Java version OpenJDK Runtime Environment (build 1.8.0_242-release-1644-b3-6915495)

[✓] VS Code (version 1.58.0)
    • VS Code at /Applications/Visual Studio Code.app/Contents
    • Flutter extension version 3.25.0

[✓] Connected device (2 available)
    • iPhone 12 Pro Max (mobile) • 44122881-8949-4230-9347-3EDC8484A098 • ios            • com.apple.CoreSimulator.SimRuntime.iOS-14-5 (simulator)
    • Chrome (web)               • chrome                               • web-javascript • Google Chrome 92.0.4515.159

• No issues found!
exit code 0

and the debug config in VSCode

{
    "version": "0.2.0",
    "configurations": [
        {
            "name": "flutter_application_1",
            "request": "launch",
            "type": "dart",
            "flutterMode": "debug"
        }
    ]
}