hihihihiiiii though (very slightly) related to my degree, this is very much along a special interest of mine and i totally didnt just spend more than an hour falling down this rabbit hole. i am gonna try to simplify this as much as possible
@kami-no-ikku theoretically, it might be able to, but from what is being shown in the study, it's more vaginal epithelial cells where there's a few sprinkled in that decided they wanted to be prostate epithelial cells instead. the vaginal epithelium (outermost layer; eg skin is an epithelium) is what is changing (mostly), but it looks like it's mostly cells that are closest to the vaginal tissue beneath the epithelium (smooth muscle, etc), so a likely course based on timeline and present factors would be that the wall lining the vagina would still be mostly vaginal cells, but the ones just underneath (still part of the "wall") would be mostly prostrate cells.
to answer @tealhairandamateurnouns 's questions, i'll start with saying that cells like endothelial cells can be very... malleable ("high plasticity"), and messengers (hormones) can come along and tell them "heyyyy so the prostate cells didn't make it to work today, anyone mind covering their shift?" and there's probably more factors relating to location+function+cell lineage (especially since this change is seen in vaginal but not cervical epithelial cells too) but some cells, will go "sure yeah why not", get a prostate epithelial cell ID pass instead, and have certain genes activated to start performing prostate cell duties instead. (hypothetically)
it's also stated in the paper that there's no visible/extremely noticeable changes here: there's no lesions eg tumors, which is why it is highly likely that these are probably just cells changing jobs.
i also say this because this ex-vaginal tissue is not all too different in that it still provides its general function as a barrier, but these new cells are noted to be glandular, aka they secrete... things that make up the fluid that becomes a part of semen (note: not pre-ejaculate): various enzymes, zinc, citrate, other nutrients. the hrt-induced prostate cells present are somewhat sparse and aggregate in "variably well-formed glands", so rather than having the vagina make prostate fluids, it's probably more like the prostrate secretions will mix with the vaginal discharge and be slightly more compositionally similar to that of semen. (which... considering the change in discharge over the course of HRT i've already noticed myself... i am refining a Hypothesis)
one last concern i've seen both in the replies and mentioned in the paper: could this potentially lead to risk of prostate cancer in individuals undergoing HRT testosterone? the answer is quite possibly: it has been observed in a similarily-presenting intersex condition, and technically, any cell that can create progeny has the potential to develop cancer. because there's no noticeable "mass" or lesion of prostate tissue, as mentioned before, you can't really check via a typical prostate exam, but for those concerned, that is not the only way to check for prostate cancer, and a diagnosis could be determined through a prostate-specific antigen test.
also. fuck knowledge being behind barriers. i downloaded the full paper for anyone who doesn't have access and put it up on gdrive.
[Image description: The first image is the Bugs Bunny "I wish x a very y" meme. It reads "I wish all trans mascs on T for 1.4+ years a very congrats on ur prostate tissue"
The second image is a screenshot of two tumblr comments. kami-no-iku asks "so does that turn the vaginal walls into one big prostate tissue lined vagina?" tealhairandmaturenouns asks "Functionally, what does that do? Does the vagina start making prostate fluids?" /end ID]
