Pause actions wont have anything to do with this - pausing can’t affect the keyboard events flowing through the event queue.
I have no idea what exactly is happening, but I suspect the problem is something “tapping” the keyboard event queue.
To have an idea of what is going on, there are two parts to understand.
The first is the event queue. Whenever you perform a UI action like clicking/moving the mouse, pressing or releasing a key), the event is not sent directly anywhere, it is added to an event queue. This is what allows, for example, you to type as fast as you want, and even if the application is slow, it will process all the keys in order in its own good time (it might not be necessary with modern hardware, but this system remains largely unchanged since the dawn of time).
The second this is that the system allows applications to “tap” this queue. Basically, when the system reads an event off the front of the queue, it has a list of applications that have said they want to see/interact with events. So in turn, it passes the event to the application, which may modify it, and then returns it to the system, which then passes it to the next event tapping application, and so on, until all the event taps have been handled, and then the event is handed to the front application to deal with.
Keyboard Maestro taps the event queue in order to steal the Command-Tab from the system (as it does not provide any override for this) and to handle capturing keys for the hot key entry in the editor.
Now imagine what happens if an application’s tap fails for some reason and does not return. Your events would start failing. There is a timeout on this system that disables a tap in this case. But a tap could also start failing by killing every event, and the system would be ok with that. Something like that might be going on.
Relaunching Keyboard Maestro Engine or TextExpander will cause them to remove themselves from the tap queue and then add themselves back, and its possible that action is what is unsticking whatever is stuck.
You could try disabling Keyboard Maestro’s Application Switcher and see if that stops relaunching Keyboard Maestro having an affect on it, but its hard to know for sure that you’ve managed to avoid any case where Keyboard Maestro will be adding its event tap.
So my guess, and its a pretty wild guess, is something in the tap system or something tapping the event queue is messed up. To tap the event queue you need accessibility permissions, so in theory the only apps you need to think about are the ones listed there, but in practice that system is so broken itself, including sometimes allowing access to apps that are not shown, that it’s hard to have much faith in it. And the problem could also be some corruption in the system related to the event processing (which is somewhat likely given that other apps should not be able to tell if another app is added or removed from the event tap queue.
Sorry, none of this really helps to find the problem I’m afraid.