That can't possibly be not true. The state has not and can not have any role in determining what is "true", if only freedom of speech has any value. As soon as the state gets to decide what is "true" and ban speech on that basis, freedom of speech is destroyed. In the USSR, there was a section in the criminal code banning "knowingly false statements defaming the state and the social order". Obviously, people who were punished under this section were ones that said anything that the communist regime didn't like, and their statements always were "knowingly false", because the same communist regime decided what is false and what is not. I don't think the US should follow this example. That's why the Constitution exists and why the First amendment is the first one. Because it's that important. Yes, the price of it is somebody can say something you don't like. You'll survive it.

Seems like a straightforward first amendment violation to me, exactly because nobody agrees on what's "true".

Defamation, for example, is not protected by the First Amendment, and deciding whether some information is true or not is crucial to determining whether it constitutes defamation.

This is irrelevant - there are all kinds of speech that are generally accepted to be outside the scope of free speech. Political speech that includes false claims does not fall under that and never has. If taking down "false speech" was something the US government can easily enforce, we'd make China look like a shining beacon of freedom. And the proper recourse to such speech is the court, not poorly paid and overworked social media moderators.

Also, it's important to keep in mind that the Trump ad in question does not make claims that are easily proven to be false - they are merely BS claims that are entirely unsubstantiated. I don't think they'd be taken down even if a rule against false claims existed and was properly followed. There's no evidence given for such claims, but not all claims without evidence are false.