He isn't transgender though. The last chapter showed that due to likely internalised homophobia and lack of awareness of lgb issues due to cultural reasons he though in order to get close to Masaki he had to become feminine and his only port of reference to being affectionate with him is man/woman relationships. You see it all the time in manga's where one man refers to himself as the husband and the other as the wife, rather than just husband/husband it's like they can't imagine a same sex couple having equality. It's pretty sad.
So no he isn't trans, and even if he enjoys looking female that doesn't make him trans either.
They're not common anywhere. I was in my early 20's when I first discovered there were others.
I think in this case the mc is, in fact, trans, because in the first chapter he says how he hates his body because it isn't like a girl body, he doesn't like his legs, arms, lower region etc. Even in the second chapter, this is mentioned again, when he wears the dress and feels fulfilled, because he can see himself as a girl, at least more like a girl. This story is more than just a romance, it's about a struggle, at least it's what I get from it.
Maybe this is also the case. I was basing my opinion on the extra chapter at the end, which is mostly text based where his insecurity over his sex were related to being attracted to a man rather than gender dysphoria which is usually present from a very age. My speculation is that he seems fulfilled over wearing dresses etc is that he thinks he will be able to pursue a relationship with the guy if adopting this persona/look but I could be completely wrong and he may outwith his relationship with the guy (sorry forgot his name, ha!) and in years to come still be assuming a female identity meaning it is not related to being validated by "the guy" therefore he may be on a transgender journey.
I think the same, but back then ppl didn't know what it was and just assumed it was homosexuality, something considered wrong so the best was to hide. Just nowadays we can see more ppl coming out and saying that they're trans, even though there's a lot who don't because they're afraid of violence and other things.
There are however, Japan, compared to most western countries, is kind of backwards regarding sexual identity issues.
More importantly, this particular story takes place in 1980, almost 40 years ago, it's confirmed in the synopsis (in Japanese) here: https://comic.pixiv.net/works/3652
The summary states something about the word "transgender" not existing back then (there were probably very very few people or none at all transitioning in Japan back then), which also confirms that Yuuji is indeed supposed to be a transgender woman.
are trans people not common in japan?