I have Flask web app that im trying to publish on azure. I deployed it on web app, Created new resource, downloaded user publish profile and published it from visual studio
I had the same issue, in my case the problem was missing redirection of the stderr, same as your code I redirected only stdout+stdin.
Adding stderr=PIPE solved my problem.
stderr=PIPE
process = Popen(exe_relative_path, stdin=PIPE, stdout=PIPE, stderr=PIPE)