Even if they were the publisher in this scenario and were liable for his comment AND their annotation, there is nothing illegal about it.

I don't think the executive action targets the fact check label on Trump's tweet specifically. I think Twitter did something that really pissed Trump off and Trump is using Section 230 as leverage and a way to extend the narrative of "Twitter is plotting against me so don't believe everything you read."

This is neither here nor there but I have considered my self a republican for the last 28 years of my life. This president's actions make me feel physically ill.

Twitter could put "Everything trump says is false!" underneath every Trump tweet and it would still be perfectly legal.