Are you running Julia by double-clicking the icon in the Finder? With all the changes in Catalina I think you might encounter problems this way that you won’t meet if you just launch Julia by typing julia in the Terminal (with a suitably configured PATH) or by launching Atom/Juno, etc.
Having used Catalina for a week now, I wouldn’t be surprised if something is asking for permission and you’re unable to see/confirm the dialog. I don’t have faith that any AppleScript will work reliably in these new conditions.
I’m also wondering why Catalina moves or copies the Julia-1.4.app from /Applications to /System/Volumes/Data/Applications/Julia-1.4.app?
Welp 1.3 didn’t have its path configured correctly OOTB, but seems 1.4 works just fine from the terminal. Guess I’ll just open an issue on GitHub for the double-click, thanks for the valuable suggestion!
What’s more interesting I think is that when I launched from Terminal I think all of the Julia instances that failed to launch suddenly sprung up, and following that the application started to work. Go figure.