Okay, I figured it out. I had been using a bad practice that I probably learned from a video a few years ago, and I never really understood what I was doing.
When I first learned how to use widgets, I was taught to create the widget, add it to the viewport, and then use the set visibility node to make it visible. What I did not understand until just now is that is NOT what the set visibility node is for. What it does is override the default visibility settings for the widget. So basically, until now, I have always been setting all widgets to visible when creating and adding them. In my one example that was " working", I just so happened to not have used the “set visibility” node.
So here is the bottom line: I was using the “Set Visibility” node on every widget (to visible), and overriding the visibility settings, thereby making every part of every widget fully visible and hit-testable. The solution: don’t do that! Thanks to all for reading this, I am sure you gave it some thought and effort, but probably couldn’t have guesses that I was doing anything that silly!