Scary story: My cousin almost killed a cyclist once after moving back to Europe after living in Asia for years. She used the horn as a friendly message (or so she thought) before passing. The cyclist, not being used to ever hearing horns on the road, got scared, looked over their shoulder and swerved out in front of the car.
I don't think I'd ever use my horn to let a cyclist know I'm there. It's hard to do a friendly, quick double-toot consistently and, as you said, it's just too loud. It's more likely to cause an accident than just waiting longer to overtake. Horns are usually a rude thing, so they're scary to hear.
Similarly, on a bike, I don't really use the bell to go around pedestrians on shared paths. Pedestrians aren't usually in the mindset of being aware of what's behind them, so the bell just makes them jump. You also can't express the difference between a friendly warning and a request to move with just a bell. Again, it's easier and more consistent to slow down and take responsibility for moving around them.
(obviously, local cultures will vary)
If you've got a freewheel, pedaling backwards can be useful; it makes a pretty distinctive, but not terribly loud noise.