Yep same here. I solved the problem for now to manually start Edge in normal mode, and after that a second edge in private mode. Then it’s working…
Problem is caused by the ‘Chrome Native Messaging Host’ that won’t start if you run edge in private mode. So running normal edge before causes this process to start and then your second browser inprivate works. See also the topic: The robots couldn’t communicate with Private mode of MS Edge browser - Help / Studio - UiPath Community Forum