Just found a solution: Refresh the page after opening DevTools
Possible reason for the problem:
When DevTools is opened, the Dart Editor reports:
The debugger connection has been closed by DevTools.
DevTools only supports one connected debugger (e.g. Editor or Chrome DevTools) at a time. Do you want to re-connect? (DevTools must be closed first)
So there might be some interference from the Dart Editor Debugger. When the connection to the Dart Editor Debugger is closed and the page is refreshed, DevTools works correctly.
This solution works for the moment, but is there a better way? Or is it a bug in Chrome DevTools or in the Dart Editor?