In the video, we use ui_accept, that is defined by Godot by default. Among other keys, pressing Enter should trigger this input event.
The game doesn't seem to switch between "Run" and "Idle". I still only get the default "text".
If nothing is happening for you, you probably missed a step. Possible and common issues include:
Could you check both of these? If after trying you're still stuck, please upload your project as a .zip file to a platform like wetransfer or google drive and send it to me. I'll check the source code directly - otherwise it's hard to know where the problem is.
I just tested your demo, and the code isn't running because your method names are incorrect in the Run and Idle state nodes:
func unhandled_key_input(event: InputEvent) -> void:
You named the function "unhandled_key_input" instead of the one that the StateMachine is calling, "unhandled_input". So your states never do anything.