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That's strange. I google a bit but couldn't found anything about them spitting.

I've been reliably informed that they leave a saliva residue on mirrors. Usually this is around mating/nesting season as they think it is a rival bird.

So, it'll spit on the competitor. 🤔

They get very territorial and can get very vicious with interlopers, even killing them, so I'm sure some saliva will be exchanged!

I've seen parent swans trying to get their own offspring to leave the nest, to the point of nearly killing them also. I've had to rescue a few cygnets in my time.