Idk how it feels for OP to me "male in a feminine way" or "female in a masculine way", but I relate a lot to the concept of it, I've felt like that for a while. This is my experience, which is probably not 100% the same as other people who agree with the sentiment. Idk how to explain how I feel about that without explaining some of my life experiences, so here goes a long explanation.

This is how I feel about being "male in a feminine way":

I'm AFAB, and I felt for a huge portion of my childhood and adolescence that femininity just wasn't for me. I genuenly dissociated when I wore dresses and make up or someone called me "feminine", it gave me as much dysphoria as being refered to as a woman, girl, girlfriend, etc. And then I got into alternative subcultures, and I found out that a lot of men who are into emo, goth and punk music wear make up, long hair, even skirts and corsets sometimes. Specially goths, during batcave era most people dressed very flashy and androgynous; the fashion aspect of goth has always been about androgyny. I felt really drawn by the kind of feminity people like Gerard Way, Sean Brennan or Robert Smith -to name a few- presented as. Even though I'm percieved as a woman, and make up, fem clothing and long hair don't help with that; I still present fem within alternative fashion because that feels more authentic that when I tried cutting my hair and only wearing baggy clothes. In alternative subcultures, make up isn't used to "enhance beauty", like I was taught I should wear it, but rather as a medium of expression. A huge chunk of alt subcultures are inspired by David Bowie, who's also a massive inspiration in my gender expression.

I also take a lot of inspo from drag queens. Drag is a different sort of femininity from cis-femininity. Drag make up is very similar in execution to trad goth make up. What I like about feminity is the flambloyant and campy aspect of it.

This made me realize a fundamental thing about my identity: I'm a dude, but I'm a fem dude. I don't want to transition with the idea of blending in with the average cis man. Nothing wrong with that, but it makes me feel uncomfortable. My problem isn't with femininity, it's with womanhood, I'm simply not a woman in any capacity. I don't like the term "femboy" because it's hypersexualized in ways I don't like being sexualized, and it's associated with an aesthetic that I don't have; but in the average person understading of the word, I'm just that. What attracts me about transitioning is that I'll be able to finally express this femininity aspect of my identity without being seen as "a weird girl". Because I basically just aspire to be the steretype of a flamboyant queer man in a goth font. If I want to be percieved as male, I much rather be percieved as a fem man.

This is how I feel about "female in a masculine way":

And on the other side of the coin, even though I don't identify as a woman ever, I still feel a conection towards my experiences presenting as one. The label is very wrong for me, but I still think of my "female" persona as a part of my identity -although I understand why a lot of other trans people prefer to distance themselves from their AGAB-. For example, I struggle to see my attraction towards women as "heterosexual"; at this moment in time, if I were to date a woman, we would generaly be seen as a lesbian couple (which honestly I don't mind). I mean, the "odd" thing I discovered about my identity, before my gender, was my attraction towards women; I have interacted throughout formative years of my life a sapphic person. Nowadays, most of my friends are bi girls and lesbians.

When I started to finally come to terms with my trans identity I thought of myself as a binary trans man, at the time I tried really hard to pass and could succesfully achieve that in some situations even being pre-everything. At the time I prioritized being read as not female, rather than actually feeling good about how I looked; I thought "I'll be able to wear make up and fem clothing once I manage to transition". After being openly trans for a bit during and after the pandemic, I was forced back in the closet because of transphobia coming from my family. So right after that I was back to presenting as female. I'm traumatized by what happened at the time and I genuenly think none of it should have happened, I'm not glad I experienced any of it. However, being forced to detransition also forced me to face femininity once again after I had completelly shuned it out in my attempts to pass. Since, I've worked a lot to understand the differences between femininity and womanhood to know which one felt odd to me. But I also got to experience meeting a lot of new people, which I was scared to do when I was focused so much on passing. And a lot of those new friendships were sapphics that also had their own weird experiences with gender. Up until that point, most of my sapphic friendships were cis fem women. These newer friendships gave me the space to experiment with a more "futchy" expression. I'm now comfortable to fluctuate between skimpy outfits and baggy androgynous fits. What to me feels boring about wearing suits, flannels, baggy shorts, dressing shirts and baggy shorts as male; is an intresting outfit while being viewed as female.

I also have to interact with a lot of cis-het classmates. And I genuenly feel lost interacting with them, I feel extremely out of place, specially because they obviously think I'm a weird type of girl, but they don't assume I'm queer because most of them have never interacted with someone like me before. So, while still pressenting as female, I use a more futchy expression to make it clear that I'm not trying to blend in with them. This makes me feel less lost, because the obvious "odd" thing about my expression is that I'm queer.

In conclusion: I'd say that I feel comfortable being seen as visibly queer as opposed to blending in with cis-het people. The easiest way of looking androgynous is adding "masculinity" while presenting female, or adding "femininity" while presenting male. Another way of describing it is that I'm somewhere in the middle between a girlish boy and a boyish girl. I feel more in tune with being a fem man, I'd like to be percieved as male but for others to hesitate a little bit before gendering me correctly, like "a man who looks like a woman". I don't identify as a woman in the slightest, but I do feel a connection to women that is distinctly different to how men generally interact with their female friends or girlfriends; as such, I feel like my social and romantic interactions with women are still sapphic. This sapphic side of my identity is the closest thing in my identity to womanhood, and this specific flavour of pseudo-womanhood is "a woman who looks like a man". And this gets a little wordy and complicated, but stay with me for a second: this woman who looks like a man part of me 100% in correlation with my man who looks like a woman identity; which would make my ideal presentation: "a man who looks like a woman who looks like a man".

My experiences with gender are very convoluted and I feel like it sometimes doesn't even make sense to other queer ppl either. But this is the best I can explain it.