Like the Horta?
I remember when the world’s first “test-tube baby” was born. It was a big freakin’ deal!
Nowadays… yawn. It’s almost common these days.
I imagine by the Star Trek era it’s nothing special at all. Which (fankwank!) is why it’s never mentioned on-screen by the characters - it’s so routine/common it’s not worth mentioning.
Baby Louise!

B’Elanna Torres was also half-Klingon, half-Human, and she had a daughter, Miral, with Tom Paris
I remembered B’Elanna’s story incorrectly. I remembered her as being 3/4 Human and 1/4 Klingon.
“Lulu.”

Like the Horta?
No kill I
I want to see a hybrid human x kzin.

Ya’ll forgot Simon Tarses from the TNG episode “The Drumhead” who was one-quarter Romulan (he had lied on his Starfleet application and claimed to be one-quarter Vulcan).
Even before that, there was Devinoni Ral in the TNG episode The Price — who explained to Troi that he’s so good a negotiator because, like her, he is “part Betazoid”: “my mother was one half, I am one quarter.”

I want to see a hybrid human x kzin
If I recall correctly, the Kzin and the Humans share some kind of interstellar microbial ancestor - so this would also be doable. Assuming that ST Kzin have a similar backstory to KS Kzin.
That episode made me wonder just how diluted your Betazoid heritage could be and still give you some kind of benefit. I’m thinking at one-eighth you might be still able to pick up some meaningful impressions from people, but at one-sixteenth whatever minimal telepathic prowess you might have would just come off as having some really terrific hunches now and then. But you probably don’t even receive that much. Memory Alpha points out that Ral grew up as one of five siblings, and none of the others had any kind of telepathic abilities.

Deanna Troi had a kid but that was a weird episode and kid and I’m not sure it really counts for this thread
Deanna Troi also had 2 kids with the very human Will Riker, as of their appearance on Picard.

If I recall correctly, the Kzin and the Humans share some kind of interstellar microbial ancestor - so this would also be doable.
In the same sense that a human crossed with a brine shrimp would be doable. The common ancestor would be quite far back.
In one of the Ringworld books, a human (or at least, a close kin to a human) contemplates mating with a kzin, but is immediately swayed from that possibility on seeing the kzin’s genitals, which are apparently completely alien to humans. No details were given, but said almost-humans were not dissuaded by mere differences in size.
Well, if Kzin are anything like house cats I can see why!
According to Memory Alpha, in Star Trek Into Darkness, Kirk is seen having a three-way with a couple of cat people. According to the producer, these were “Caitians”, and the wiki goes on to explain that these are related to Kzinti much the same way Vulcans are related to Romulans (i.e., more or less the same species or genus, it is mostly the culture that is different).

In the same sense that a human crossed with a brine shrimp would be doable. The common ancestor would be quite far back.
I would assume cat people count as mammals?
Caitians have been Star Trek canon ever since the animated series, which had a Caitian named M’ress as part of the bridge crew.
One notable difference between them and Kzinti is that Kzinti females are unintelligent (basically, just sapient enough to be able to say “I’m horny; fuck me”). Though one of the Known Space stories does reveal that that’s a relatively recent development in Kzinti evolution.
And any resemblance between Kzinti and Earthly mammals is either coincidental or convergent evolution: In Known Space canon, the common ancestor of the two (as well as most of the other lifeforms in the Galaxy) was a species of algae cultivated by the Slavers for food.
Lower Decks (the animated Star Trek series) features a Caitian doctor as a regular character
Doctor Angry Kitty is one of my favorite characters on the show.
I was under the impression that the Kzinti only showed up in that one TAS episode that seemed more like a crossover with Niven’s Known Space, and that it contained other historical changes that didn’t fit the Star Trek universe. So I’ve always interpreted it like the Marvel/DC crossovers: a different universe where both exist simultaneously, and not actually a part of the prime timeline.
They’ve never shown up in any of the live-action material, which is what is usually considered canon. But they have shown up in various extended universe material, such as novels and role-playing games. The animated series has always been kinda-sorta-canon-but-not. The episode Yesteryear, for example, seems to be pretty widely accepted as canon. For licensing and rights reasons, though, the Kzinti can’t really be fully canon.
I don’t know if they can “legally” throw them in whenever they want willy-nilly, but the wiki says that in Star Trek: Picard they had explicit permission from Larry Niven. They were only mentioned as a threat and did not show up on-screen, though, IIRC