Basically I'm creating a tiny button on the side and I want it to not get focused when clicked.
So for example if the user is on some random application, they should still be able to type in that application after clicking on my tiny button window without having to click on their application back again.
The only way I know to have an app running without taking the whole focus is to define your app as a "background" app.
To do so, add
<key>LSBackgroundOnly</key>
<string>True</string>
to the Info.plist (which is located in your macos/Runner folder)
This solution has some drawbacks though, but at least you'll have the behavior you're looking for.
It's tough to understand your requirement without knowing your code snippet. but for now, let's try this link maybe you get your answer there
https://pub.dev/packages/macos_ui - For UI
https://docs.flutter.dev/development/ui/advanced/gestures - For Gesture detect
https://blog.logrocket.com/handling-gestures-flutter-gesturedetector/ - For Handling tap
Perhaps this is what you are looking for?
https://api.flutter.dev/flutter/widgets/IgnorePointer-class.html