Since the umbrella is so visible, they may see it from further away during one of their brief glances at the road.

How do you know if you're seen when carrying umbrella? Eye contact is not enough (info you can find in pretty much any driving handbook).

You don't, but it's almost certain that you'd be safer with it than without.

Cyclist here. In my experience a horn works best if the driver is distracted. This is one major reason I have an air horn on my bike.

The umbrella is for the AI. For drivers there’s always eye contact

Eye contact is only meaningful between drivers. When you are asymmetrically squishy (as a pedestrian or cyclist), some drivers will take eye contact as "good, they have seen me, they will know to stay out of my way".