I am proud of you for trying to improve your condition through therapy and medication. Truth is, there are those of us for whom these things don't do much if anything. There's no shame in that. Clearly, this is a problem for you, so I hope, however it is resolved, that you can finally find a way away from all this misery.
As per your feelings on inadequacy, I don't think you are worthless -- you've proven you're a strong and determined person, it's just no amount of strength and determination is going to drag you out of suicidal ideation. If most of what you experience is suffering, then it is a very valid desire to end that suffering. After all, we allow dogs - man's best friend - to have their suffering by way of euthanasia. Why we should either be so cruel towards humans or so inconsiderate of the canine's wish (as we are the ones to decide their death), has no real rationale to it. You're also not a burden, just a suffering individual.
I suspect you too cannot access legal assisted suicide, which I can empathize with.
Failure is always a possibility -- with any method. Death, like life, is a gamble. I know, because I gambled on the wrong things, and couldn't work up the guts to try more successful solutions. It's a scary thing knowing you might end up with brain damage, or just... go back to suffering as you did before. You're not incorrect about wrist-slitting. It tends to take a while and I'd imagine quite painful initially. That's why I could never do it. Hanging can be traumatising if someone walks in on it -- but then, I guess suicide is traumatising no matter what. If you could part on your own terms and give people closure before you passed, that might soften the blow, but obviously, that's not a possibility. If you do opt for hanging, I would recommend preparation and research (there are various threads and topics on this site and even scientific articles and youtube videos that can give you an idea of what a lethal dose of something may look like and what the side-effects are. Medicine, you see, works on that precarious knife edge of allowing people to stay alive and allowing them to find the means to die. The latter of which... I actually don't think is that bad, but maybe that's because I'm not a pro-lifer.). Failure might end up being worse than success. So careful consideration -- for any method -- is a good idea. Whether or not you end up going through with it. And, don't blame yourself if you back out last minute or if it fails. You're not at fault for having a survival instinct. It's one of those things most of us are born with.
If you find you cannot do it, maybe consider changing up treatment? What you're using is clearly not working, but maybe there's still something out there. It's an alternative, I'm not suggesting you should. That's a choice that lies with you... and I also make no promises that it will work. (There are suggestions out there for alternative treatments and whatnot, though, and maybe informing the person you are seeing for therapy that the medication still leaves you with these severe depressive episodes might help find better ways, but if you feel like the person your visiting wouldn't understand or hasn't been very helpful or empathetic in general, no pressure.)
Being born is not a choice you make. I just wish dying was one. Maybe it's an unpopular opinion on mainstream sites, but people should be allowed to die on their own terms, with dignity and respect. You're not the cause of anyone's suffering -- all you're doing is dealing with the consequences of a lot of bad luck, and someone's/some people's decision. So please do not blame yourself. As for you thinking you do not deserve to be alive, a) that was decided for you beforehand by those who brought you into the world, so clearly, it's not a matter of deserving and b) as mentioned before you are neither worthless, nor a burden, and don't cause suffering. And, even if it's gonna sound depressing, your suffering led you here, and it's something people here can relate to. You (probably) make people feel less alone. (I know you make me feel less alone in my circumstances.) There's no need to believe me on this -- if you distrust me, that's fair.
You mention struggling to work -- would, some sort of freelance job, or something from home, potentially be the answer? Something with maybe less of a tight schedule? Or would it only make things worse?
