Snopes has a piece on the pins: https://www.snopes.com/news/2025/04/16/trump-golden-pin/
Carr is clearly wearing a huge golden Trump pin in the picture posted on his official Twitter/X page.
But I agree that the details from the Snopes discussion suggest there's little evidence of a "mandate" for his cabinet to wear one as per the title of the blog post I linked.
I concede the point that with regard to lapel pins the evidence only points to the lapdog-like obsequiousness of the FCC chair at this time. ;-)