>"What does the split feel like?"
Actual MK-Ultra victims might be able to correct me here, but from what I understand the personality split occurs when one has a traumatic experience so earth-shatteringly horrible the human mind has no coping mechanism sufficient enough to deal with it.
As it's usually abuse aimed at young children, they're even less experienced about the world, which means they have practically zero coping methods.
A victim, being often confined or controlled (EG police, lawyers, officials, etc are all 'in on it') doesn't usually have the option of escape usually available to other people (EG suicide), the mind does the only thing it can: it fragments.
Essentially, what they end up doing is putting all of their abuse experiences into 'one little box', which allows the mind some semblance of functionality - one side is 'normal' and apparently 'unabused', the other side so grieviously abused it functions in ways we cannot comprehend.
What MK-Ultra handlers do, from my understanding, is fragment those parts further. So first they have 'Alpha' - which is a bit like having a 'formatted harddrive', then they 'install' others (Beta, Theta, Gamma, Omega, with Epsilon and Upsilon being rumoured) who serve different purposes.
From what I could piece together, Beta is sexual (a play on the Alpha-Beta theorem), Theta is anti-Christian (it's unclear what exactly that does), Gamma is a 'security module' that makes sure the other personalities are not tampered with, and Omega is 'suicide' - to prevent discovery.
In literature, the switching of personalities is signalled by the terminology of 'hats'. So Beta, for example, being a 'sex kitten' persona, is triggered by 'the cat in the hat'. There's also an assassination personality (one of which remains unidentified to me) which is triggered by catcher in the rye, which mentions a line: 'this is my shooting hat, I shoot people in it'.
So in my estimation, the split feels like such a soul shatteringly, emotionally traumatic experience that it belies any sort of descriptor.
I think the closest any person will experience is emotional heartbreak in relationships, but my opinion is that is a mere 1/10000th in comparison of depth of pain (the pain is so bad, it triggers amnesia in the victims: each personality, for obvious reasons, is unaware of each other).