Oh, I was planning to do a whole post about "how much sick is enough sick to be justified in wanting to die?" (But I'm too shy for that atm), so I feel I can answer this!
Obviously I can't speak for any of the people on Tiktok, but this is my view on it. Killing yourself, many times, will cause a lot of suffering around you. So, in a way, to get over the guilt of causing that pain around you, I need to feel that I'm sick enough, that my suffering is enough that causing pain in other to end mine is justified. In a way, I must be sure the pain I'm escaping must be greater than the pain I'm inflicting on others.
Another thing I feel - though it's disconnected from suicide, and strictly tied to the current medical system's state - Is that a lot of illnesses cause unbearable amounts of pain but don't really get you a proportional amount of empathy, benefits, etc. For example, I assume that if you have the big cancer you'll get taken very seriously by doctors, get empathy from your relatives, medical paid leave, etc. However, many other "invisible" illnesses can also cause you huge amounts of pain and make your life unbearable (I'm thinking MS, endometriosis, IBS/IBD/SIBO...) , but because of the fact that they're not considered "as bad", "as deadly" or "as serious" you will be gaslighted by doctors, and considered "just lazy" by the people around you. Those illnesses are also less studied, so while there may be treatments available for cancer and a hope of getting better if everything goes well, you may be out of luck with those invisible, "lesser" illnesses.
I was personally suffering for a whole year before any doctor started believing my pain was real, because my pain ended up being from one of those "lesser" illnesses, and thus "not pain enough".
In those cases, it makes really sense that you'd wish you were sicker - at least, you'd get proper medical attention.