Along the same lines you noted the contrasting customs between Ashkenazim and Sefardim, Rabbi David Sperling writes:
There are different customs about standing or sitting for Kaddish. The
Rema writes in his additions to the Shulchan Aruch (O.H. 56, 1) "One
should stand when they answer Kaddish". This is, as you wrote in your
question, because it is counted as "words of holiness" ("dvar
sh'bekedusha") which should all be stood up for (see the Rema ibid).
However the Mishna Brurah there writes that there are those who say
one does not have to stand for Kaddish, unless one was already
standing. So, for example, the Kaddish after Hallel, when one is
already standing because of Hallel, one should remain standing. This
is how many Sephardim rule (see Yalkut Yosef, volume 1, p. 95). The
Mishna Brurah rules that one should be strict and stand for every
Apparently, the custom of sitting may stem from not being obligated to stand, as Hacham Gavriel quotes "The Arizal was not Makpid to stand during Kaddish (Shaar Hakawanot Daf 16 Amud 4 based on the Kaf HaHaim 56:20 and the Sefaradi Aharonim all agreed to this Pesak)."
For more information which might shed more light in general, see here and here.