Writing a Flutter Web application, I try to leverage a Web-UI-Testing framework based on Selenium. Sadly I fail to identify a HTML-Element representing a certain flutter widget
I do not think it is right way to use any Selenium kind of testing framework for Flutter Web.
Reason for that is that you (as web developer) have no control on how generated DOM looks like. Which means you can not use XPath and other means to select elements.
I suppose the only way of testing Flutter apps (including Flutter Web) is using Flutter Driver: https://api.flutter.dev/flutter/flutter_driver/flutter_driver-library.html