If compelling this speech is a First Amendment violation, wouldn't the prohibition on outright saying you got the warrant also be a First Amendment violation?
No. US law makes a distinction between 'prior restraint' and 'compelled speech'.
Prior restraint is the government forcing you to _not_ say something.
Compelled speech is the opposite, forcing you _to_ say something.
Both have a high bar to meet, and meeting one does not mean you that you meet the other. In the case of compelled speech, I don't believe a US court has ever ordered someone to lie, which is what would be required here.
