I finally got curious and went digging, looks like public and private; at least, I don’t see anything distinguishing between the two in either this text or the proposed rule

Also looks like the two conservative chairs voted against the rule lmao, shocking

Ed, I did find this in the finalized rule under part E, Sect 1 , ‘Generally’

For example, the Act exempts “banks” and “persons, partnerships, or corporations insofar as they are subject to the Packers and Stockyards Act.” And the Act excludes from its definition of “corporation” any entity that is not “organized to carry on business for its own profit or that of its members.” The NPRM explained that, where an employer is exempt from coverage under the FTC Act, the employer would not be subject to the rule. The NPRM also explained that State and local government entities—as well as some private entities—may not be subject to the rule when engaging in activity protected by the State action doctrine.

So probably just certain contractors/researchers could still be bound by NDAs under this ruling, likely ones for government work (as mentioned below)