Why is "suicide" the fundamental problem of philosophy, for Camus? Surely the fundamental problem of philosophy is more traditionally how to live, not how to die. Even if we allow the centrality of death in any mature philosophy, the art of dying, as Nietzsche suggests in places, always seems a lot more arbitrary than life. Suicide may be uniquely human, at least universal among humans, not something waiting to be discovered or invented, only thought about, but as far as I know Camus was not even suffering much beyond anguish at his failures, so why the centrality of it? Is this thought that happy people have missed something important and are actually living inauthentically? There may well be some truth to that, but then to deny the same fact of sad, even suicidal, people seems wrong. I actually agree that tackling the issues that suicidal thinking brings can make you stronger, but then I don't think that it's the realisation "I ought not die" that affirms life, but its precedents.
I've been suicidal, don't worry, not now, for a variety of reasons. I suppose the sanest was that, when it's over I mean nothing at all, and I want to mean nothing at all, if only to hurry it up, as if returning to who I really am. But it must be a mistake to say "this is my true self", the self that seriously contemplates suicide.
Anyone saying it has nothing do with death and is just a means to live better may end up trying to force trivially wrong metaphysics on people (but there's no "ultimate" reason to go buy food) to escape the fact that suicide is not just a matter of 'life'.