Resident cat being aggressive with new kitten

So I recently got a kitten that is very well socialized as my cat was/is very understimulated. We try to give him all of the attention he needs but everyone in my household works a full time job so he’s at home by himself a lot, which led me to believe that it would be good for him to have another cat living in our house. He is very poorly socialized and was a stray before we brought him in.

We’ve been giving them supervised play sessions, but he often plays too rough with her. He bites her neck the second he’s within reaching distance to her (which I’ve read that that’s how they establish dominance so I’ve been letting him do it) and she’ll hiss and growl and he’ll back up and stare at her but if she moves he’ll lunge at her again. It seems that there has been no positive play because he plays too rough every time.

How can we encourage positive play? We separate them when she screams because she’s obviously done but he’s not. He’ll sit and meow relentlessly at the door after separating them. What can be done? Do they need bribery (snacks, toys, etc.)?

We initially introduced them through the carrier when we brought her home and then we kept her in our bathroom for a week. After that we had some supervised “play dates,” but stopped for a few days because our cat threw up a bunch one night due to stress. During these “play dates” we would separate them when he started biting because she hissed at him every time. I wasn’t aware that he needs to set his boundaries but it’s obvious from her body language that she does not have fun during this “play” and he seems overly aggressive and is more so aiming to hurt her rather than play.

After a few days passed I read that we should let them set their boundaries so we let them play, but once again, it was obvious that this play was aggressive and she wasn’t enjoying it. There was an instance where he wouldn’t stop chasing her and biting her and she screamed loudly so we separated them and haven’t been allowing them near each other since. He really seems bent on interacting with her and there have been multiple times where he tries to run through the door the second I open it to try and get to her. I’m really afraid that he just wants to hurt her and isn’t interested in playing.