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.