GC leaning but not 100% GC here. I can definitely see the argument that trans people are no longer their birth sex. As you said we have those 5 characteristics we use to determine sex, but at least some, but not all, of them can be changed. Now sex is ultimately a binary (there are only X and Y chromosomes, and only eggs and sperm, no other options), so strictly speaking if you're born [fe]male then you will always be [fe]male for the rest of your life. However, some people view sex as more of a strongly bimodal spectrum. They would argue that a fully transitioned trans woman, for instance, is at least partially biologically female due to no longer having a penis (external genitalia), and having hormones closer to that of a female (HRT). Whether those are achieved artificially or not doesn't matter; for instance if a person was born missing a leg and was a wheelchair user, but later in life got a prosthetic leg, we wouldn't continue to view them as a wheelchair user and we'd call them a person with two legs in casual conversation, though we would be remiss to pretend that a prosthetic leg is literally exactly identical to a natural leg. The people who focus on "vaginoplasty is an inside out penis" are technically correct, while not colloquially how we would think about such a procedure. Let's say you're a burn victim and you get a skin graft from your buttocks to your face, we wouldn't say "This person doesn't have a face, they have a part of their butt that they put on their face", even if that was technically the case. So in that sense, at least on a conceptual level, I understand the idea that a trans woman can be considered to be at least partially "biologically female".

I have a few issues with this concept, though. As you can see from the metaphors above, a thought exercise I often do is, "How would we talk about this condition if the person involved was not trans/"gender identity" was not a factor?". And that's where things get a little dicey and IMO the insult to the dignity of non-trans people outweighs the insult to the identity of trans people here. Because if we start saying someone can be "more [fe]male" or "less [fe]male" due to the presence or absence of sex characteristics, we're now making claims about a good number of non trans people. For instance, it would imply that women who've had a hysterectomy are "less of a woman" than women who do still have their uterus. It would imply that a man who lost his testicles to cancer is "less of a man" than a man who has testicles. And of course, it means that intersex people can never be "fully" male or female. And maybe, depending on how you define sex, that is technically accurate? But it seems like a big insult to the dignity of people in these conditions, the same way calling a vaginoplasty an "inverted penis" or a skin graft a "butt on your face" would be. So in that sense to me it comes down to ethics, and I am not comfortable using this "spectrum of biological sex" as a way of conceptualizing biological sex. I think it's better to say you're either biologically male or biologically female, and that a biological [fe]male can have many varied traits.

Then we have to ask ourselves how useful is "sex" as a descriptor, considering that it implies a wide range of possible traits? Part of the question too is whether sex is something set once at birth that can never change, or if changes in the body should be considered in updating our definition of a person's sex. In over 99% of cases, sex is determined at birth by the presence of a penis or vagina. If the person removes that organ, does it still make sense to refer to a descriptor of their condition that was based on that organ? If you're born sighted but later lose your vision, you are no longer considered sighted, and you are considered blind, even though you weren't born that way. Would it make sense to exclude such a person from services for the blind on the basis of being "sighted at birth"? I do think that there is room for some updating of our priors when it comes to describing a person. However, does that have to be done by updating our descriptor of their biological sex, especially when every last trans person retains at least one (chromosomes) trait of their natal sex? Take in healthcare situations, information such as "has had a vaginoplasty" or "is on a course of female hormones" would influence the appropriate medical treatment (eg: not giving a testicular cancer screening, or considering the hormones when prescribing medicine). In that sense though we can just refer to those specific conditions; sex alone doesn't tell us enough info (I mean, with over 99% accuracy, you can assume a person whose biological sex is listed as male is going to have a penis, but strictly speaking you don't know for sure until you physically examine the patient).

Now to more directly address your question about a person who has changed ALL of their sex characteristics, including DNA. I'm pretty utilitarian in my philosophy so to me these thought exercises aren't super useful. It reminds me of the "if you could implant a trans woman's brain into a biological woman's body, would she be a woman?" thought experiment. We could speculate on this, but in reality the odds of such a situation actually happening are so low that for me I'd rather spend time thinking about situations that are likely to happen. If there's some evidence that changing chromosomes is going to be a possibility in the future, I'd be interested in that, but my first thought would definitely go to helping correct chromosomal conditions such as Down syndrome, rather than trans issues.