The extension is originally intended to work in the launch mode only. However, by using the custom configuration (Python C++ Debugger Custom: GDB) and modifying the Python config's (type = 'python') request to attach, it becomes possible to attach to an existing process. Python C++ extension is initially stopping the Python extension and waiting for the C++ debugger to get attached before restarting (continuing) the Python debugger. The issue is that Python debugger is not continuing even after the corresponding message to continue has been sent.
The same issue, with the Python debugger getting stuck, is also sometimes coming up using the regular launch mode, especially on Windows.