It's difficult and I can see this from a lot of different view points.
As a SM:
If DP is regularly putting responsibility on you, and not wanting to involve SS actual mum, then you need to draw a very clear boundary. I would do this 1 day, but make clear that going forward DP needs to ask DM in future or another family member. Football stops until SS is more stable OR DM has SS on a Saturday to facilitate this. You should be a back up option, not the default.
Everyone needs their downtime, please also recognise that you do too. This situation will be having and have already had a huge impact on your relationship, lifestyle and even just regular routine. You can't pour from an empty cup.
DP should ideally be asking his employer for a reasonable adjustment on this 1 occasion, given he deems it a crisis. Any decent employer would understand.
If SS is in crisis, there also needs to be a very clear and agreed plan between all parties of how toilet breaks/ showers/ time alone are to be managed any time he is in your care. Don't minimise how much of a huge responsibility it is on you.
DP can also reach out to social services for respite. This doesn't mean SS will be under longer term care of social services, but rather they can provide daily/ weekly/ monthly respite services to parents who are managing challenging children. You can contact them yourself, have a GP do it or school safeguarding leads can refer.
As a professional (with experience of suicide watches and managing those actively wanting to die, as well as dealing with successful suicide attempts):
There is no watching in the world that will prevent someone who really wants to take their life. I have known an individual on 24/7 watch (literally not a second alone) who cut themselves secretly and nearly bled out, using a mattress to disguise what they had done. Another who self strangulated under a duvet whilst on 24/7 watch using their own hair. I've known hundreds of individuals be checked on whilst on observations smile and wave hello, to be checked on a minute later close to death. It can literally take seconds.
Generally speaking, those who are successful in committing suicide are the ones who don't tell anyone they are feeling that way. That isn't to say your SS isn't in crisis and should be left alone in the house for hours, more that it is a positive he is telling you both his feelings and wants help.
Please do not go around the house hiding everything but a speck of dust to minimise risk as a PP suggested. Someone who is intent on dying will use anything. The more you minimise, the more panicked state an individual gets into and the more risky and irrational their behaviour then becomes. Yes, remove access to anything obvious, but those intent on doing it are far more imaginative than someone who is not in that mindset.
What are the school doing to support?
What is the GP doing to support?
Have you or DP done any self referrals to MH services, for you both and for SS?
It's great there are so many PP who say they would step up and help no matter what or who it is. Please don't minimise this situation for OP and others who have had to deal with this as being selfish or uncaring unless you have been there yourself. It is a huge responsibility to take on and everyone needs their downtime. You cannot ever imagine the mental and emotional impacts this kind of situation has on an individual. Anyone would struggle to live in this situation 24/7, even when the crisis period was over. And I say that with extensive experience in a professional capacity and knowing how to manage these situations. I can't imagine what it is like when you have limited experience in what to do or look out for.
I hope things get better for you all OP 💐