I really don't understand the paranoia around employee surveys. In 20 years as both an IC and a manager I've never seen them used in a way other than described.

If your manager wants to fire you they don't need to create a complicated ruse to get evidence that you're unhappy, or that you have opinions or think that they are a bad manager. None of which are anywhere near a justification for firing, anyway.

In fact, at most companies, telling your manager that you're unhappy and looking for work elsewhere is more likely to get you rewarded with a promo or bonus.