Sanity check on my cat introduction to assuage my worried household plz.

Tl;dr:

Me: Adult
Country: USA
Vet info: Don't need it for this issue, but I have an easily accessible vet.
Main issue: Sanity check to make sure cat introduction behavior is within normal parameters; cat is hissing and growling at kitten but does not attack and seems to be slowly de-stressing though still averse.
Cat age: 3 years and 8 weeks
Cat Sex: Female/spayed, and male/intact, respectively (yes we will get the little boy neutered when the vet says)
Financial: Yes we can afford a vet but again, this is a simple behavior check.

Longform:

The context is that I have an Old Cat (irrelevant to this scenario) and a young cat, and Old Cat is not spry. Young Adult Cat needs someone to pester and wrestle with that isn't Old (Tired) Cat. So, we got a kitten for her to play with and keep her busy when we're not around to play (which is daily, we are around a lot, she's just a ball of energy).

When I was a kid (longer ago than I'd like), my country-folk parents did the simplest of cat introductions: put the cats in the house and let them sort it out. This has literally never failed for my family. The idea of a slow weeks-long intro baffles me. But, because I've felt like I should Do It Right now that I'm a grown ass woman and introducing this new kitten really matters to me, I did the standard recommended introduction that everyone online talks about.

We are now in the "let the cats meet" stage. I have already gone through The Process: put Kitten in a room of his own; let Cat sniff Kitten's scents through the door and do the obligatory irritated phase; swap some blankets between Cat and Kitten's room; feed Cat and Kitten on opposite sides of a closed door; give Cat plenty of love and treats; let Cat and Kitten stare at each other through a crack in the door. Cat is now willing to accept the smell of Kitten on the house's human residents and on blankets Cat will interact with. Cat has also started going into the part of the house that has Kittens door and hanging out with us as if nothing is wrong. When Kitten yelps for attention, Cat will scoot off back to the rest of the house.

So, we let them meet fully. Cat started by immediately fucking off across the house to hide. After a few more encounters, Cat is grumpy when she knows Kitten is around, but she does not attack Kitten. Still, she does sit around emitting sullen growls, hisses when Kitten gets near, and spends the entire time Kitten is out, watching for Kitten and grumping at anyone who bothers her, including her pal Old Cat.

I think that this is great progress. Cat has gone from "panic-hide and avoid the entire upstairs" to "sit with us and not under the couch, sounding offended about life," and even let Kitten get within 2 feet once without bapping. Kitten got one bap when he got too close, and then he left her alone, chastised, for a time. He tends to respect her boundaries when she hisses. She gets tired of him trying to approach after a while, and we put him in his room when that happens, and give her treats and praise. Hell, Cat has never tried to hurt Kitten, she just seems anxious and butthurt that we let another cat into the house that isn't Old Cat.

My partner's condition for getting a new kitten is that we can't name him, get attached to him, or assume he will live with us permanently until Cat accepts him in a way that does not look hostile or worrisome. My partner absolutely does not want a situation where we have to confine two cats to separate areas of the house. Is this a normal progression of cat introduction? Is Cat doing normal cat things? Again, I'm used to "fuck it, throw 'em together and let 'em figure it out" and this has worked for me against all odds and so I am a weirdo who has never observed the slow process. He is so scared that she didn't immediately accept Kitten the way Old Cat did (who gives no fucks) and that this is a bad sign and thus she will never accept Kitten. I want either some fodder to tell him that he can chill out, it looks good so far, or for someone to tell me that this really isn't going to work and I should rehome the kitten while he's at the age everyone wants their new cat to be.

Thank you all for putting up with my wall of text!