I can relate to some of these feelings. Especially the parts of not feeling like life is for you and that people will only truly understanding the extent your distress by going through with suicide.
However I would not ever discuss these feelings with my therapist. I’ve been badly burnt by him reporting my suicidal ideation to my GP against my wishes in the past. I disclosed a previous suicide plan I had nearly gone through with a few weeks before, but didn’t actually do it and stated I did not have any imminent plans to hurt myself. He told me he would not report, then spoke to his supervisor, changed his mind and wrote to my GP without my consent.
It caused a massive massive rupture which we are still not fully out of 5 months on. Things are much better but I would now never take the risk of talking about suicidal ideation with any therapist.