I wrote a response to @wanderers-idol tags under the Hornet outfits drawing, but I really liked the question asked so I thought I'd make it into its own post (hope you don't mind!)
The reason for Hornet not having a Deepnest/Weaver outfit is because, in the AU, she was there for only about 2 years before Herrah became a Dreamer, and at the time she wore very simple clothes that she'd quickly outgrow anyway. Hornet moved to the White Palace and lived there afterwards. She had no reason to visit Deepnest, her mother was gone, and the other Weavers were not particularly fond of her. Unlike Herrah who was willing to trust Vyrm for the sake of the kingdom, including the Weavers which she wanted to protect, they did not see Hornet as Weaver enough to treat her as one of their own.
Consequently Hornet did not visit Deepnest pretty much at all after moving, and feels no attachment to it. Which is a big element of her grief that she still deals with to this day, there is a part of her that fears her mother would be disappointed in her for abandoning her kin and her birthplace, and it pains her that she's never going to get the chance to ask. She visited Deepnest a few times after Vyrm's disappearance, but all the Weavers have died to the infection or left since then, so she only stayed at her mother's resting place for a bit and left.
FPK Hornet's story has been largely written before Silksong, so her connection to Herrah, and consequently the whole three queens thing is very different here. Instead, a big part of it is her grief at not knowing her mother pretty much at all, which I suppose is at least faithful to the part of Red Memory in which Hornet can't recall Herrah's face. There is a pain she feels, and a guilt she has to deal with, that because they separated so young, she doesn't really feel a connection to Herrah. Similarly, she had no idea there was anything going on between Herrah and Vespa until she learned about it from Vyrm years later, so she only saw the Hive queen as a mentor, not a mother figure, and by the time she realized that was her only real connection to her mother, Vespa has unfortunately died. And her relationship with the White Lady is complicated, she doesn't really see her as a mother, and she doesn't have the most fond memories of the time she interacted with her when WL was still in the palace (she separated with Vyrm and left at some point). So while she respects the Lady, she has no desire to build a relationship with her. Herrah was her mother, the White Lady did not even really know her. Hornet appreciates her efforts at trying to be a mother figure for that brief time before she left for the gardens, but that's about as far as it goes.
Basically, the FPK AU Hornet is definitely more, let's say White Palace oriented, specifically connected to PK/Vyrm. By that I mean that it's where she grew up, and Vyrm is the one who raised her to the best of his ability. But something I do like to explore is that, after Vyrm disappeared and she had to live on her own and survive in the wilds, her whole appearance became more "wild" and less White Palace proper. She got attached to her red cloak, which I designed to look very similar to the one on my Herrah design. A kind of "she doesn't even know how much like Herrah she is" thing that adds to the grief of her not knowing her mother.
I also like to think that she was able to wear that red cloak at the time of Vyrm's disappearance because, with the White Lady gone from the palace, Hornet felt less pressure to "look proper", and Vyrm let her wear whatever she found the most comfortable. Maybe he knew it would be important for Herrah to see her daughter find her own identity, so now that there was no other voice to overshadow his, Hornet was able to choose her own wardrobe.
In a way, the cloak that was eventually destroyed was her Weaver outfit. But its destruction does not erase her Weaver roots, quite the opposite. It was something that shaped her whole identity. You can see that in every outfit where she did get a say in its color, red is the most dominant color. It's her favorite hue, just like it was for Herrah. And I think her living to be an image of her mother is a beautiful way for her Weaver heritage and her connection to her mother to shine.