These are all things having little to do with suicide: Japan completely disarmed everyone outside of government in the 90’s, and they have better access to healthcare than Americans, but suicide rates only grew.

Japan's suicide rate remains substantially lower than America's suicide rate (particularly with respect to men) according to WHO data. this is particularly noteworthy because of Japanese cultural attitudes toward suicide (seen as morally neutral or honorable in certain circumstances, rather than consistently reprehensible as in America). it would imply the disarming you're talking about is putting a significant damper on the rate.