But "no hope" is not equivalent to "extremely depressed".
Think of people who commit suicide over inescapable scandals, chronic pain, or terminal illness. Extremely depressed comes with 'no hope', but that's cancelled out by 'decreased agency' (which is one theory for why antidepressants carry suicide risk). Not every form of hopelessness shares that loss of agency.
*Excluding hospital assisted suicide where someone OD's on pain medication under end of life pain.