I've noticed that the kaddish printed in most editions of the gemara and mishnayos includes ויצמח פורקניה ויקרב משיחיה (vayatzmach purkanei vikareiv meshichei), without annotations such as "nusach sefard".
Is it possible that Nusach Ashkenaz, which omits this phrase in other versions of the kaddish, includes it specifically for the kaddish said at a siyum?
I have seen Nusach Ashkenaz siyum reciters say "Veyatzmach". According to this article, it seems appropriate for everyone to say it. There are 5 types of Kaddish and the one recited at the end of a siyum is the same one recited at a burial. It is called Kaddish Hagadol. The article states:
The final type of Kaddish (Kaddish Hagadol) is recited on two special occasions: when
making a siyum upon the completion of a tractate of Talmud or an order
of Mishna, and at a funeral. These two occasions are radically
different, but there is something in common. The theme of this Kaddish
is that, in the merit of Torah study, the world will be renewed,
including the eventual revival of the dead. Therefore, it is
appropriate for both a siyum (recognizing as it does the rewards of
Torah study) and a funeral (as it contains within it the consolation
that those who have passed on will someday return to us).
I have been to many (Nusach Ashkenaz) siyums, and have never heard the person say "VaYitzmach..." The siyums that I have been to include by alumnus of YU, Chofetz Chayim, and Lakewood. All are predominantly Nusach Ashkenaz.
I wonder if it is because you are in Eretz Yisrael where Nusach Sefarad is common that you have seen this written.
The Koren Talmud Bavli explicitly said that it is only said for Nusach Sefarad.