You’re getting a hard time here, OP.
A few things strike me. What comes across in your posts is that you feel resentment for the situation and guilt that you don’t love your step son. These two things probably feed each other in a bit a vicious cycle and I think you need to release yourself from that cycle.
First, the resentment. You need to change the focus of this. If you feel resentment toward your SS, you need to remind yourself that that feeling is misplaced, you cannot blame the child for seeking out the safest home for himself, in fact that is to be commended. It is not his responsibility to ensure that the adults in his life are happy, he has no reason to behave any differently, he is doing the right thing. If you resent the mother, you need to remind yourself that you have absolutely no influence over her whatsoever and any energy used in wishing she were different or would suddenly step up is wasted. The only person in this situation that you might resent, although you don’t say you do, is your DP and here you could actually insist on a change. You say you pay pay for everything, do all the cleaning etc. If this is the case, no wonder you feel resentment, you’ve just landed it on the wrong targets. Go to your DP and change things there, if he as nice and kind as you say then he should step up.
Secondly, you do not need to love your step son and you do not need to feel guilty for not doing so. When he is under your care, you need to feed him, clothe him, make sure he’s clean and has what he needs, you need to ask about his day, smile at him, give him a level of affection he is comfortable with, show concern if he is ill or upset, but you do not need to and cannot force yourself to feel love towards him. You can do all those things I’ve listed without loving him. I was a teacher for many years and I am fortunate that I always felt quite bonded with my students but I had a mentor who did not, and she explained that she just had to fake it for those students as they all deserve to feel that special connection to their teacher. This is harder for you as he is with you all the time, but it is not impossible and is what your SS deserves. You can release yourself from the guilt of not loving him if you are doing all you can for him otherwise.