Is supplicating for death due to an unwillingness to commit suicide and be eternally damned to Hell, coupled with a hatred of life and oneself, considered an act of despair, and thus sinful?

It is not permissible to wish for death due to harm. A Muslim should be optimistic and think well of Allah, and supplicate: "O Allah, keep me alive as long as life is better for me, and cause me to die if death is better for me." One should seek the causes of happiness in their life, the most important of which are striving in obedience to Allah, engaging in permissible recreational activities that dispel worries, being content with what Allah has decreed, entrusting all matters to Him, achieving and excelling in tasks, and seeking Paradise after death.