Do you think a woman and man speaking out in favour of sex are given the same treatment?

the same treatment? Maybe, maybe not, I don't know. But I hardly think that a man bringing fourth the exact same arguments wouldn't have them dismissed as bigotry either.

Transactivist here have supported the abortion bill that passed last December and the previous law proposals regarding this, too.

Of course they were. Why wouldn't they, given what the legal situation regarding abortions was before (going of your description)

I wouldn't say this totally altruistic of them because they also make sure the bill used inclusive language despite that only a woman would ever need an abortion.

do you know what happens when inclusive language is not used? There was a case where a transgender man that was pregnant and in need of an abortion was denied said abortion, because the law in question spoke of "women who are pregnant", not "people who are pregnant" or "women and other people who are pregnant". The transgender rights movement was argueing for the law in question to be changed to fix this oversight. Gender Critical feminists were fighting against this change, meaning they were literally forcing this man to carry a pregnancy against his will. That is why inclusive language is important, and it is a lot more than mere "hurt genderfeelz".

There is Mara Gómez, a trans natal male who was allowed to play in the top division of female football. He was treated like a brave hero by local media. There are other cases of trans natal males competing in female categories, but Gómez is the most famous one.

if transgender women have to compete in the mens division, does that mean that transgender men are having to compete in the womens division - even after having been on hormones fopr year? Because there is a case like that, where a transgender men, that had been on HRT and wanted to compete in a contact sport in the men's category. He was forced into the women's category, because the rules were, that the divisons were based on birth sex. Due to the hightend muscle mass resulting from HRT, the transgender man was signigicantly stronger then his competitor, resulting in his competitor being injured. Then this story was taken by gender critical people and misrepresented in such a way, that readers were left under the impression, that this had been a case of a transgender woman beating up some vastly outmatchend non-transgender woman.

Besides how it affects women, there are other problems with this law in particular regarding minors. Under this law, any minor can request to change of the sex marker of their document with the approval of their parents. Kids as young as 5 (five, yes, five, this is absolutely not a typo) have been allowed to do this.

and what does changing ones legal gender mean in practice (other than changing what is on the passport - by the way, the personal ID in my country doesn't even list gender or sex)?

But what does being seen and treated as a man means? Is only about being told "yes, you're totally a man"? Or is there something more?

That, when you look at them, you perceive them instinctivly as sex/gender whose gender identity they are, and act acording to this perception. So, essentially, a transgender women/transgender man wants that, when a onlooker with no knowledge of them being trans perceives them, this onlooker perceives a woman/man, and treat them like the onlooker would treat a non-transgender woman/man doing the same things.

I remeber that there was a post about the mixed feelings transgender people experience over poor treatment based on being perceived as the sex/gender whose gender identity they are (say, for example, transgender women experiencing sexual harassement from men (mixed, because it is simultanously feeling bad over the poor treatment and feeling good over being perceived the way they want to). For the transgender men, I don't recall what their experiences in this regard were about, but there were some). So for the gender-non-conforming (gender non conforming relative to their gender identity that is) transgender man example, imagine him walking by an onlooker, that despises crossdressers. If the onlooker perceives the gnc-trans man as a man wearing a dress, the onlookers reaction will be very different from them perceiving a woman wearing a dress. So, if this onlookers reaction will be in line with perceiving the gnc-trans man as a man, the trans man will be left with this mixed feeling, on the one hand succeding at being perceived the way he wants to, on the other of course the negative feeling from being treated poorly. For positive or neutral actions obviously there isn't such a negative feeling, meaning the general feeling is not mixed. (Note: I chose negative treatment arising from being perceived as the sex/gender whose gender identity they are to clarify, that this is not about politely pretending that the transgender man is a man, but about there being no such pretense).

Note, that there is also the desire, that, if the transgender person informs other people over them being transgender, people don't start treating them differently because of that.