Watermelon pieces are made mostly of water, but are solid as a whole, not liquid. You can't pour them. And if you actually blend them into a liquid, then you get watermelon juice or soup. (Soup vs beverage is a distinction based on the mode of serving, in a glass vs bowl+spoon)

I think my main issue is that the spectrum goes from

entire melon -> salad -> slush? -> beverage

with decreasing side length of the cut pieces.

So both the fixed structure from your definition (" Salads are dishes without a fixed structure") and solid/liquid definition don't feel really tangible to me. YMMV