This was answered, in part, in your prior post although you added details to that, as well as this post, which changed some things. For example, your original post said nothing about her being abusive or there being a court order for no contact.
To repeat and to clarify: no one gets to decide who the other parent is with. Unless there's a criminal or neglect element, it's irrelevant. If there is, you get a court order. It's ridiculous to ask if you can cuddle or feed the baby. Yes you can.
What's so totally ridiculous in this situation is that you say the bio mom is irrational and controlling, there's been a court order in the past, and now your boyfriend and she think they can work this out together. He asks her to legalize the custody and visitation arrangement, and she freaks out and threatens him with not seeing his son. So ALL THE MORE REASON to start the legal process. Your boyfriend is woefully uneducated about this whole legal situation, so instead of actually finding out how to set it up, he gives in to her control. He's either misinformed, he's intimidated by someone with a long history of being irrational, or he actually WANTS to be in this kind of contact with her.
There are red flags here. Instead of insisting that he at least consult a family lawyer or mediator, you ask questions about feeding.
I don't want to be harsh here - just firm. None of the 3 of you is qualified to evaluate this situation. You cannot "work things out" with an abuser. Everyone with a brain tells an abused woman not to believe anything that the male abuser says. Why would it be different with a man being abused by a woman.
Give your boyfriend one week to contact a family lawyer or a mediator and set an appointment to actually learn something. The mediator can try to set an appointment with his ex after the meeting with your boyfriend. If she attends, great. If she doesn't, then the mediator (or someone else in the firm) can become your boyfriend's lawyer and start the process.
If he does not do this, then your relationship is doomed. Get out. You cannot have a future with a man who is too weak to break away from drama that will affect this child for the next 18 years. The definition of insanity is continuing to do things the same way and expecting a different result. His talking to her isn't working. Your continuing to "support him" by reminding him to pay bills and saying you don't agree with her control over him isn't working. And your continuing to post this question on the internet, with the same responses from all the moms here, isn't working either. It doesn't matter what we think - we have no control over whether your boyfriend listens to his ex and allows her to control him.
If he doesn't straighten up and take decisive action, you have a good indication of the kind of man he's going to be with you.