> So even if said intellectual property (AI-written code) is not copyrightable, it's still a trade secret.

It's only a trade secret as long as the company takes reasonable steps to protect it, and as long as what is being protected is a reasonable thing. Even if the code is legitimately a trade secret, if an employee publicly says "That code looks to me almost exactly like this GPL software" then (assuming the employee is correct) any court would take a dim view of a court case against the employee, because stealing shit is against public policy.

> This is doubly stupid because

No, that part really isn't. Trade secrets are about general business stuff, and as long as the company isn't asking you to help them hide evidence of malfeasance, they can ask you to keep any stupid shit secret.