I timed it and it took around 10s. Sometimes faster sometimes slower, definitely not super quick. But it’s not blocking the screen so you can at least do something else while it’s running.
I looked at the shortcut to see if there was maybe anything malicious and there’s an action that it doesn’t recognize and is prompting me to update shortcuts, but I’ve got the most up to date version.
Guessing that’s a part of the problem for you too.
Edit: looking at an OP comment, I’m guessing it’s a call to the chatgpt ios app, which I don’t have.
I wonder how hard it would be to do this tampermonkey or similar cause then you could send the request when you open the link then you wouldn't have to wait as long