Python launcher Icon every time a script runs
Well, it sure seems the difference is caused by different methods of installing Python. If your systems are identical then its caused by Python itself. You could try installing python via homebrew on your new machine and see if the behavior changes. You should run python in a virtual environment. If you do that you can have multiple versions of python3 on your machine.
How are you running Python?  If you run it from the command line you may not have this happen. Are you trying to stop this behavior or are you just curious why it happens? If you are trying to stop it then use the file you link to in your question.