New cat advice

Hello! I just adopted a new baby girl (Honey) to add to our family. I already have a baby boy (Cosmo) around her age (1) that we adopted about two months ago, but he is very much so a social boy. We realized Cosmo needed a friend so we adopted this beautiful orange tabby. Honey is a sweetheart and very affectionate, although a little sick. She’s just done fighting off an allergic reaction according to the shelter and still had a little bit of remnants of cat acne (we got her ceramic bowl and stainless steel water bowl, per recommendation) but otherwise she is very sweet and loving.

I did notice even at the shelter that she wasn’t vocalizing much at all. She was very quiet compared to the other cats. That’s all fine, as my first cat I ever adopted (she was 6 when we got her and she’s a loving angel), wasnt very vocal at first either.

However, we brought her home and kept her in her own room. Honey was in my room and she was doing really well! She was being very affectionate and the staff member at the shelter even showed me how she loves being held and she does! Problem occurred when I was trying to go to the bathroom and slowly opened my door. Didn’t see anyone, but as I opened the door more, Cosmo ran around the corner and sprinted into the room. He’s very very good at being sneaky and really fast, and ran in. My girlfriend came running after him and we both went “oh no..” especially since Honey has only been here for a few hours.

Thankfully, because Cosmo was from this cat cafe for the other shelter in the town, he was a LOT more well behaved than we thought he would be. We knew he was good with other cats and knew how to properly.. introduce himself to others but worried maybe he was going to be territorial now. Honey immediately went under my bed and hissed at him a couple times. Cosmo was being a very nice gentleman and sat in the complete opposite corner as her and just stared at her. He even got low on the ground and just sat there. At one point my girlfriend (who was observing them while I made dinner) said Cosmo even showed her his belly and stayed away, as she hissed at him every time he tried to get close. She even closed her eyes and rested a bit while he was still in the same vicinity too.

When we could, we got Cosmo out and she’s been alone since. She stayed under the bed for a bit but eventually came out and was affectionate with me again. Now Cosmo sits outside of my door and meows like crazy. If he even noticed us going near the direction of my room, he will sprint, but we have been extra careful of not letting him in and make sure he is either in my girlfriends arms or in her room before opening my door.

I have two questions regarding this matter, one, what should we do differently about the introduction process if they already know of the other’s existence and saw each other so quickly? I know Honey was said to be good with other cats, but obviously she’s in a new environment and she’s still a bit sick so she would be more wary of this strange, energetic boy. Two, Honey is very loving with me, she rubs against me sits on me, headbutts me but I’ve only heard her purr a little bit for a very short amount of time. She has not meowed either at all. Meanwhile, cosmo meows like crazy and is very vocal. One different between the two is that cosmo was a shelter cat, born in a kill shelter and rescued by the shelter we adopted him from that took him in. Meanwhile, Honey was a stray before going to the shelter. The staff members at the shelter never said there was a problem with her quietness, but I’m just a bit worried at how she doesn’t purr even when being extremely affectionate. Is this an issue, or am I just being a worrywart? Are some cats just more quiet with their affection, and prefer immense physical affection instead?

Edits: typos and added detail