Just searching on the entire last paragraph...
“No common or contract carrier shall require or cause any label, tag, or other written notice to be placed on the outside of any package, luggage, or other container that such package, luggage, or other container contains a firearm.”
...pulls up numerous references from the NRA-ILA to the BATFE.
I think you nailed it. Delta is in violation of federal law.
I would guess this is a knee-jerk reaction to the FLL shooter incident. Likely “suggested” to Delta brassby a deep state official in the ATF or FAA. And, of course, Delta didn’t have the balls to fight it.