The legal definition of disparagement is closely related to a freedom of speech. In order to disparage, legally, you must make a statement that is false, injurious, and derogatory. That’s actually illegal in perpetuity with or without signing that statement. You can’t make a false, injurious, derogatory statement about an organization.
On the other hand some companies have attempted to change the definition of disparagement to mean something else. For example “you can’t say anything bad about your experience at the company.” Nope, sorry, that doesn’t fit the legal definition of disparagement. If you say something bad about your time at the company, which is true, it’s not disparagement. It’s a right according to your freedom of speech. And you can’t sign away that right. However, even this gets misunderstood.
A corporation does not have to allow you to say anything you want without repercussions. They just can only hand down repercussions that they have access too. For example, if you were to say bad things about the company you work for that are true, they do not have to continue to employ you. Or ever employ you again. That is their right. But they can’t say that you can’t say those things. They also have the right to attempt a civil action against you for disparagement. They may win or lose.
So anyway, are you over reacting? Maybe. I doubt that any paper about disparagement would actually change any of your rights in any way at all.