Note:
Already existing triggers such as typed text string ",sometext", or existing triggers "CMD-1" do work.
Typed strings can be assigned, no issues there.
If I delete the "CMD-1" trigger, I can't assign it back again.
I would still guess that Secure Input is Enabled as what you are getting is the exact symptom. Either logging out and logging back in or a restart should fix it. Or even just putting the screen to sleep for a moment or two usually fixes Secure Input for me.
Also check for any Chrome (or similar) tabs that might be waiting for a login, a 1Password "unlock" window, and so on. There's a bunch of things that don't get reported by those ioreg commands.
Please forgive the very basic question, but in your screenshot the hotkey field still says Click. You are first clicking that field and then trying to enter your hotkey, yes?
That might work, if you mean, say, other automation/shortcut apps.
Maybe first create a new user account, and try KM in that. If it still does not work as inspected, that would suggest a low-level problem, such as a reinstallation of the OS being needed. If it works, you will know that the problem is caused by something in your usual user account.