I haven’t claimed it doesn’t imply fragility too. Just that the uniqueness is the primary meaning of it - thus the term snowflake. “I’m unique and thus deserving of special treatment”
If it was primarily about fragility then we’d probably be using some other term as that is not generally the first feature that comes to mind about snowflakes.
I feel like you googled the word and consider that truth without really looking at the nuance of how the phrase evolved.
Long ago, there was a saying that “no two snowflakes are alike.”
Decades ago: We personified it to promote diversity. “We are all individuals, just like snowflakes!” The point of this was to get people to look past stereotypes. People weren’t defined by their ethnicity, they were individuals and you should judge them for the person they are, not by their appearance.
Within the past few years: Conservatives use the term sarcastically. Delicate snowflakes, try so hard to be unique but melt if you look at them wrong! Meaning, instead of fitting in, they want to be different, but when we bully them for being different, they get upset.
So, yes, it’s about uniqueness, but when used as an insult, it’s more focused on fragility.