All symbols are wrong, but in ways that oddly make sense:

• Mint - it’s a leaf.
• Fedora - it’s a wearable.
• Debian - the logo coils itself, so does a snake.
• Arch - arcus~arco~arc is “bow” in Latin/Romance.

I don’t know if what I’m going to say is correct, but this smells like LLM shitting emojis.

Seems in that place a Fedora is worn on the chest instead of head.