I feel this in my bones. For all those recommending sleep training - it just doesn’t work for some babies. I tried and tried and tried to sleep train mine using a variety of methods for weeks at a time and he did not sleep longer than three hours (and only longer than two hours a handful of times) until about 19 months. He still wakes several times a night, and I am often up for the day around 5.
All this to say: I get you, OP. I hear you. None of this is your fault or the result of choices you did or didn’t make. Some kids are just wired this way, and people whose kids slept, even if they woke up a couple of times a night, just won’t get it.
However, suicide is not the answer. I also felt suicidal, but what got me through is thinking about my little one growing up without a mum. I couldn’t do that to him.
Ignore the well-meaning advice from people who haven’t been there (I felt my lowest after three straight weeks of sleeping no more than an hour at a time and four hours a night while trying to sleep train - don’t even try to go there). Focus on maximizing your sleep any way you can. If you need to go to sleep at 7 to get a few more minutes in, do it. If you can, nap. Get help if it’s available - relatives, friends, partner, anyone who can look after LO for an hour or two while you sleep. It is truly hell. And do call Samaritans if you are thinking seriously about it.