as someone who knows a lot about TERF discourse second hand (not a fan of personally engaging with them) - TERFs are more likely to say “transwoman” than “trans woman”. I don’t have a proper citation but I’ll try to walk you through the logic of it
what “transwoman” implies is that it’s not a “real woman” (never realwoman, of course). It subtly excludes trans women from the title of “women” by making the word itself seem like it’s some sort of third option, not a real woman, not a man, a “transwoman”.
trans inclusive communities nearly always have the space, that’s because trans women are simply a sub-category of women, and not something different altogether.
though nowadays you’re also likely to see more outspoken TERFs say “TIM” which stands for “trans identified male” (they mean trans women)
bottom line is, in online spheres trans friendly people and sources will almost always have the space, and trans exclusive people and sources tend to write that as one word
it’s the same sort of linguistic shift that prompted the trans community to stop using “transsexual” move to “trans[gender]” and now “trans [gender]”. Even though in essence they all mean the same, some of them have been used by groups that hate us much more than others. (For a similar example see “stupid” > “retarded” > “special needs” > “special” > “intellectually disabled”. All the words before “intellectually disabled” are medical terms turned insults, and honestly i’m not even sure if “intellectually disabled” isn’t halfway there already)