OP I think it is highly, highly likely that his dad or his bit on the side have been telling your DS13 about this. There are a few things that stood out to me to make this apparent;
- He's using adult financial and relationship grievances to challenge your parenting. He is using terminology and references that he should really not know much about;
- A typical teenager might say, "Why can't you buy me those trainers? You've got loads of money!" But this boy is asking where "his dad's payments" are going.
- He's framing your work travel as evidence that you might not be committed to your children.
- He's describing your spending as irresponsible because of money you supposedly "received in the divorce."
The last point is especially interesting as he's not annoyed you won't buy him something he wants, he is making a moral judgement about your usage of money that he THINKS you have.
So, where has he acquired that narrative?
Possibly his dad, OW, conversations he's overheard, or his own interpretation of things he's been told. However, my suspicion is that someone has given him a version of events in which you are financially privileged, selfish or somehow indebted to his dad. He is very much repeating an adult narrative on the version of these events. I would suspect them both, especially your awful XH given his behaviour thus far.
People not wanting you to tell him about the 50:50 is interesting, and I agree, but not just for aforementioned reasons (that I've read so far) by PPs. His dad doesn't want them 50/50, he doesn't want to have to pay for the nanny, and has honestly probably told him that he can't afford to see him more because you "won" all the money in the divorce. Your DS knowing the truth would be crushed tbqh, but I think it is important for them to know who their parents really are to save a shattered image later down the line, or to not risk the potential of them idolising them and thinking their behaviour is okay. However, in this case given the circumstances, don't.
The secondary reason that I would not tell him is because, especially given his attack on you so far, it will likely backfire onto you.
Imagine being 13 and hearing that your dad would have spent more time with you if your mum had paid for a nanny. He could interpret that as rejection, feel compelled to defend his dad, or become angry with both parents. He doesn't need to be shielded from reality forever, but he shouldn't have to carry the emotional weight of adult negotiations about his care, and that is above all else most important.
I think ultimately there are a whole host of things at play here. He might be angry about the divorce, resentful of you, protective of his dad, or struggling with the fact that his dad has a new life. He might feel that criticising you demonstrates loyalty to his dad. Divorce really does mess with kids heads more than many people care to realise.
Honestly what I would do OP is give it to him straight about the finances. His behaviour towards you is unacceptable and completely unfair given how much of a disgrace his 'dad' is. Just don't mention the 50:50 thing because it's not fair on him. Let him ask questions and answer honestly. Be honest about everything, he will value that more than sweet nothings to make him feel better, but just be cautious. In time I am sure that he will see his dad for what he really is and want little to do with him. Carry on being his rock and his safe space. It's ironically a good sign he is venting his anger to you because you make him feel safe enough to do so. I doubt he does with his sperm donor.