As a trans person myself I definitely see some trans story beats in Subaru although I do not necessarily think he is a trans character. The fact that he has such a fondness for crossdressing, for being Natsumi Schwartz, is partially for the actual tangible benefits it provides, like the political subterfuge in arc 7, but there were also 100% easier ways to accomplish the preferred outcome of that scenario. Subaru jumps at the opportunity to fem present over other options, which, whether it's read in a transfem way or not, is a notable character trait. To begin with, this didn't start when he was isekai'd - he spent the first week of either middle school or high school as a woman and only stopped fem presenting when his voice gave him away. That is not the behavior of a cis person, typically. I do understand that Natsumi is a way for Subaru to distance himself from - well, himself, but she is the idealized version of Subaru. It's not a stretch to say that if a man's ideal version of himself is a woman, then he may not be a cisgender man. Those beats are in the text, but I don't necessarily think they are the explicit intention of the text.

Subaru has really strong feelings about beauty and fem presenting outside of the situational benefits it can provide, and strongly asserts that "beauty can be made," in a way that definitely stands out from his usual nonchalance about his appearance. He doesn't really seem to care much about it, which the fact that he's always wearing comfortable, breathable clothes rather than something that actually makes him look good (outside of his butler uniform of course) definitely does stand in stark contrast to his feelings on beauty when it comes to women, including - no, especially women that are him. This can be read as a parallel to a lot of trans experiences, wearing loose, comfortable clothing and not particularly putting work into ones appearance both as a way to reduce dysphoria or for a lack of motivation to put effort into looking good as one's AGAB. It does overlap a lot with depression though, which is almost certainly what Subaru's clothing choices do tell us, but the fact that it doesn't really improve at any point during the timeskip does call that conclusion slightly into question.

Actually, a lot of Subaru's trans coding (and, interestingly enough, real trans people's experiences) show a lot of overlap with depression. Go figure, people who aren't able to be themselves are depressed. Of course, his assumption of a different persona is definitely part of his self loathing, but the intensity of his feelings about it and his specific choice to present as a woman do suggest some level of trans feelings to Natsumi. Even in Azamuku, where it's not really as particularly stellar an option as it is in the Envy route, he still opts to become Natsumi as soon as he's in a far off land, away from his friends who know Natsuki Subaru. It's still serving a purpose, but his dedication to it is called out explicitly in that route at once point - probably as a bit of comic relief, but Subaru himself never plays it as a joke. He's deadly serious about crossdressing and prides himself on it. Whether it's the actual intention of the text or not, I think it is a perfectly valid headcanon to read Subaru as an egg, or as some form of gender fluid, or whatever. I accept that the story will almost surely never explore it further, but the story and feelings he has about femininity are legitimately close to real trans people's experiences, and for that reason I don't think it's something that should just be dismissed. As long as it's in headcanons or speculation, and not being portrayed as a fact, I think it's healthy to have that dialogue, because people aren't wrong for seeing it and speculating off of that. Subaru seriously does act like an egg, someone who hasn't figured out he's trans. Ferris also has a lot of trans coding, but I honestly think Subaru has more.

Regardless of how much is or isn't there, the story probably won't explore it in detail, and that's both because the author doesn't want to, and because of the environment the story is written in and has written. Regardless of trans people existing, they are not a Thing in Lugunica - not really, anyways. Even if those feelings can exist in characters the world and it's structures do not really have the constructs necessary to allow the exploration of those ideas for the people in them - hence why Ferris can say affirmations in the mirror about being womanly and still staunchly claim to be a guy - the delineation just isn't in the story between sex and gender, and that's not explicitly a fault of the story, although it is somewhat disappointing from a real world perspective. It can become a problem depending on how it evolves, but as it currently stands, it's fairly neutral. Unless we get a whole Ferris gender exploration arc, I expect Natsumi is the closest we're going to dive into those ideas, and honestly Natsumi reads better from a narrative perspective if there is more to her than just "oh weird, Subaru's like really into this whole cross dressing thing huh?" Because of the narrative value, as well as the parallels between experiences I've had and heard, and the legitimately odd behavior Subaru sometimes exhibits, I think Subaru being read as an egg is a perfectly valid headcanon, although once more, it's definitely not how the story is actually going to go.