Absolutely vital to start from desired outcome and work back in terms of finding out whether a grievance is the best route.
If you want to improve the situation at work I would say that’s probably an unrealistic aim, as it sounds like something which is ingrained and cultural and won’t be solved by (say) disciplining/removing one manager or similar.
I’d say probably the outcome which is likely to be best for you is finding a new job. A classic mistake many people make is to resist a particular course of action/outcome because they think that is what their employer wants. It may well be true that your (or anyone’s) boss wants to get rid of you, but that doesn’t mean that finding a new job won’t also be the best outcome for you.
Staying in a job or taking a particular course of action to try and teach your employer a lesson is rarely a good idea imo, and usually has far more of a negative impact on the employee than the employer, regardless of the result.
If you think you’d be able to find another job relatively quickly/easily, I’d probably concentrate your efforts on that rather than devoting time, effort, headspace and emotion to raising a grievance.
If, on the other hand, finding another role might be difficult/take a while, then a grievance might elicit an offer of a settlement from them which would give you a bit of a cushion.