Cat introduction advice - Kitten and Resident Cat

I wanna clarify a few things before I get into more detail just to help y’all get an idea:

1) I grew up with dogs, I didn’t start owning a cat till October of last year when my resident cat (her name is Milo) showed up on my front porch begging for food (no one was looking for her. I believe I live near a cat dumping site). I mainly mention this to clarify the little experience I have with cats, but I have been binge watching Jackson Galaxy like crazy over the last couple of months.

2) I recently found a kitten (I named him Peter) on the side of my neighborhood road (I’ve seen 0 posters and nothing about him on Facebook nor lost pet websites). I didn’t have the heart to leave the poor kitten there especially with how skinny and friendly he was. First thing I did was drive to a shelter only to find out none of the shelters in my county take in strays. The only one that does has a very high kill rate. I didn’t have the heart to risk it and it was a Sunday so it was closed anyways. I took the kitten to the vet the following Tuesday to get vaccinated and tested for the various feline diseases (all came back negative with a clean bill of health). No chip. Vet believes him to be 11-12 weeks old.

3) The timing isn’t good. We’ve been renovating the apartment (which is now done outside of painting) so Milo has already been stressed. Now she has a little brother who she is bothered by despite him being held in another room. Unfortunately, she has seen him multiple times. The first time was because I didn’t know they shouldn’t have had any visual contact, and ever since it’s because Peter is sneaky and gets past our legs to run into the living room.

5) Both cats are on a feeding schedule with a small snack in between. Breakfast at 8:30am, dinner around 7pm. Snack is around 12 or 1pm.

4) I have watched multiple Jackson Galaxy introduction videos but still feel like I have some unanswered questions, so here I am.

My question mainly revolves around positive association. I have been doing the feeding on either side of the door and doing my best to site swap, scent swap (beds, socks, etc.), and give treats whenever she sniffs his belongings to establish his scent = food. On Monday and Tuesday, she was somewhat reluctant to eat. This was mainly due to Peter getting out before dinner (he stayed in during Breakfast). Wednesday we saw improvements although he got out again. Three times. Thursday and today she hardly huffed/growled while eating her meals. She isn’t eating all her food, however, but I acknowledge it’s due to the kitten being around. We noticed improvements after we started leaving Peter in the bathroom and letting Milo start eating first because sometimes she needs to be convinced to eat. Once she starts eating, he’s allowed back in the bedroom to eat on the other side of the door from there. After dinner, we take Peter upstairs and let Milo walk around the bedroom to get used to his scent some. We of course let Peter hang out in the living room (Milo’s home base) after 4pm until dinner time cause Milo requires some outside time or she gets upset.

I just don’t know if I’m doing this completely right. Although she has stopped hissing at the smell of him, she is still growling and or huffing when she goes in the bedroom or sniffs a scent soaked sock. Am I wrong for giving her a treat when she sniffs but proceeds to growl? Am I just encouraging her to growl? How exactly do I know when I can do the screen door/ gate technique? Peter could not care less about the things around him, as he is a kitten. But of course Milo is stressed out and I don’t want to try visual again yet. She does not attack when she sees him luckily, but will swat at him (not gently at all) and hiss and growl. Today is the first day we managed to keep Peter from going in the living room as well. If you have any tips, I would love that.

Sorry for the long post.