Also of note - suicide in the US is extremely difficult if you've been identified as someone with intention. You get checked on every 15 minutes, including at night (which can be a torture by itself)
As far as the US is concerned, you've quoted policy. I'm pretty sure that jails and prisons in the US are supposed to provide medical care, mental health care, food enough for decent health (without having maggots): There are plenty of examples of it not happening. "I didn't know they were suicidal" or "We've been short staffed, and I couldn't check on him" are easy excuses.