It’s just that the meaning has been watered down. As you saw in the dictionaries, “unique”'s first definition is “one of a kind”. It’s an absolute. It’s also self-contradictory for something to be more “one of a kind”. Now, as you note, it’s just a high-sounding synonym for rare or unusual.
I’m a potter. I throw nine cups and a bowl. The nine cups are all very similar, as I am a very good potter, but still unique as each cup has minute differences in shape, size and thickness. The bowl differs far more greatly than the cups by virtue of being a bowl. It is more unique than the cups. I don’t see what’s so hard about this.
And, FYI, unique took modifiers a lot before the 1800s, so you could say that it was originally watered down, was arbitrarily restricted and has since been let free to resume its proper breadth of meaning.