Hyperlinks are not accessible while the process is still logging

While a process is still logging in the console, the previously added hyperlinks are not accessible.

To reproduce, use the attached project and run the Main class as a Java Application.
Then try to click on a hyperlink while the application is still running

Project to reproduce the issue on:
[Test.tar.gz](https://github.com/eclipse-platform/eclipse.platform.debug/files/11476281/Test.tar.gz)