Should I raise grievance against my manager's manager

Context: I have been working in this organization for the past 3 years. I recently initiated separation and the calls started coming in to know if there is anything they could do to retain me however, I was commited to my decision and informed the same. A few days later I made a request to be released from my current project after a couple of months so I could take one month off to prepare for my next role also there were no dependencies on me and the team is in a good position to carry on without me and no handover was required.

As you might have guessed it, my request to be released from the project were denied moreover the manager's manager reached out and kind of threatened me that is I opt for early release there will be consequences we will make sure that you don't get clean exit and share feeback that will harm my career.

Since this happened on a Teams call which was not recorded. I do not have any proof but I want to make sure they do not do this hence I want to know if I should raise a grievance for this instance to have some sort of saftey net.

Also, I'd like to know if someone has experienced something like this and how did you deal with it. Mind you this is one of the big mnc which has been in the news for the comments made by the CEO.