A trans woman (i.e. a person born as a man who later transitions to a woman) who likes women is homosexual, yes.

Homosexual = attraction to the same gender as one's own

Heterosexual = attraction to genders unlike one's own

Sometimes, it's less that a trans woman becomes gay when she transitions, and more that she already was homosexual in her attraction before she transitioned. A lot of transfeminine sapphics have described being attracted to women in a gay way before they identified as a woman. The same goes for straight transfems who didn't feel like their attraction to men was gay, but got lumped in as gay because of their assigned gender.

It should also be said that "attraction changes" that happen from hormones are often more absolute than relative based on gender. It's more like someone who wasn't attracted to men before suddenly is, or that someone who didn't feel sexual attraction to anyone now does. Sometimes it's just that you're more comfortable being who you want to be, and sometimes it's your preferences actually changing. It redefines your relationship with your body, identity, and sexuality change in ways you don't expect.

I'm also not a native speaker but my language/country operates under similar enough "rules".

On top of what other people have said, cultural identifies, e.g. lesbian, can have a more specific and inclusive definition/understanding at the same time, for example in relation to non binary people.

There are also more precise terms in use inside the queer community than can be helpful to communicate with others. You have a look at finsexual, minsexual, sapphic, or achilean, for exemple. Labels in general don't gather that much consensus and are more useful as a self descriptive thing.

Another aspect is the sex is just like gender socially constructed, and we only choose the terms male/female to designate people based on a loose list of physical characteristics, and those choices are arbitrary. Same thing with hono/heterosexuality.

Words like homosexual aren't really in fashion anymore, although if I needed to describe myself to someone without much awareness I could describe myself as a homosexual transgender woman but that wouldn't be my first choice.

Also, I think we can all understand that when people are looking to learn, they might not have the best language yet but I appreciate your disclaimer. It's usually preferred to only use their actual gender (the one they will tell you, rather than the one under was assigned to them at birth) when taking to/about trans people. Saying something like trans man or transfeminine people, respectively a trans person that feels and want to be considered as a man (is a man is what I would say when not trying to explain things) and a trans person that is transitioning towards more feminity (that can be a trans woman or a feminine non binary peeson, amongst other things), will be enough information for people to understand without having to misgenger anyone.

I hope I'm making things clearer instead of more complicated.

Your confusion is totally valid and it also confuses a lot of native speakers. Along with what yellowbadbeast said, It's also not uncommon (but becoming a little old fashioned) for people who don't fall in "traditional" gender norms to just use the label queer to describe their dating preferences to avoid confusion