You are in a very difficult situation. My DS is ND and has MH issues which sparks self harm. He is 23 now and has matured, but at 17/18/19 he was tricky and it was wearing trying to get the balance between not enabling but also not wanting to create unnecessary issues.
I think you have a great opportunity now to implement changes, as he has shown he is capable of behaving in more appropriate manner.
I would suggest a conversation with him and DGP along the lines that he seems happier and in a better place mentally at DGPs and you are very happy for him to remain their for the foreseeable. You could even offer to contribute a small amount to his food costs etc. (Your costs will probably have gone down as he is not eating your food, using your electricity or using your fuel). Reiterate that you are happy for DS to return home when he feels ready, but you will not tolerate the previous disrespect or threats of suicide. You might even offer to attend some family counselling with him to work through what is behind the disrespect and the suicide threats (mainly to be seen to be doing the "right" thing, rather than a particular desire to participate, but it might be fruitful).
And also it's time to stress that he needs to start to take responsibility for himself and if he comes back then he will need to continue to claim UC or get a job, as you cannot and will not continue to support him financially, especially with the lack of respect.
My mantra for a few years with DS was that if he wanted to be treated like an adult then he had to behave like one.
We are out of that phase now, he got a job when he was 21 and has been there nearly two years and is a very easy soul to have around the house now and he happily contributes to the household costs. We still have self harm issues and a constant trail of ND chaos, but the rude, obnoxious version has pretty much gone.